--- /dev/null
+This is the documentation tree for NLopt.
+
+Markdown (.md) files for NLopt documentation live in $(top_src_dir)/doc/docs.
+
+To build and visualize the HTML documentation locally using the
+mkdocs package (useful for verifying on your local machine before
+committing), install the `mkdocs` package, then run the
+following command from the top-level meep repository tree:
+
+% mkdocs serve
+
+and then open the following URL in a browser window:
+
+http://127.0.0.1:8000/NLopt
+
+This launches a little web server on your local machine
+plus a filesystem hook for rebuilding the documentation
+tree automatically whenever any .md file is modified, so
+you can see what the actual HTML documentation looks
+like in real time as you edit the source.
--- /dev/null
+---
+# Citing NLopt
+---
+
+If you use NLopt in work that leads to a publication, we would appreciate it if you would kindly cite NLopt in your manuscript. Please cite *both* the NLopt library *and* the authors of the specific algorithm(s) that you employed in your work. Cite NLopt as something like:
+
+- Steven G. Johnson, The NLopt nonlinear-optimization package, <http://ab-initio.mit.edu/nlopt>
+
+The authors and appropriate citations for the specific optimization algorithms in NLopt are listed in the [NLopt Algorithms](NLopt_Algorithms.md) page.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt Algorithms
+---
+
+NLopt includes implementations of a number of different optimization algorithms. These algorithms are listed below, including links to the original source code (if any) and citations to the relevant articles in the literature (see [Citing NLopt](Citing_NLopt.md)).
+
+Even where I found available free/open-source code for the various algorithms, I modified the code at least slightly (and in some cases noted below, substantially) for inclusion into NLopt. I apologize in advance to the authors for any new bugs I may have inadvertantly introduced into their code.
+
+Nomenclature
+------------
+
+Each algorithm in NLopt is identified by a named constant, which is passed to the NLopt routines in the various languages in order to select a particular algorithm. These constants are mostly of the form `NLOPT_{G,L}{N,D}_xxxx`, where `G`/`L` denotes global/local optimization and `N`/`D` denotes derivative-free/gradient-based algorithms, respectively.
+
+For example, the `NLOPT_LN_COBYLA` constant refers to the COBYLA algorithm (described below), which is a local (`L`) derivative-free (`N`) optimization algorithm.
+
+Two exceptions are the MLSL and augmented Lagrangian algorithms, denoted by `NLOPT_G_MLSL` and `NLOPT_AUGLAG`, since whether or not they use derivatives (and whether or not they are global, in `AUGLAG`'s case) is determined by what subsidiary optimization algorithm is specified.
+
+Many of the algorithms have several variants, which are grouped together below.
+
+Comparing algorithms
+--------------------
+
+For any given optimization problem, it is a good idea to compare several of the available algorithms that are applicable to that problem—in general, one often finds that the "best" algorithm strongly depends upon the problem at hand.
+
+However, comparing algorithms requires a little bit of care because the function-value/parameter tolerance tests are not all implemented in exactly the same way for different algorithms. So, for example, the same fractional 10<sup>−4</sup> tolerance on the function value might produce a much more accurate minimum in one algorithm compared to another, and matching them might require some experimentation with the tolerances.
+
+Instead, a more fair and reliable way to compare two different algorithms is to run one until the function value is converged to some value *f*<sub>A</sub>, and then run the second algorithm with the minf_max [termination test](NLopt_Introduction#Termination_conditions.md) set to minf_max=*f*<sub>A</sub>. That is, ask how long it takes for the two algorithms to reach the same function value.
+
+Better yet, run some algorithm for a really long time until the minimum *f*<sub>M</sub> is located to high precision. Then run the different algorithms you want to compare with the termination test: minf_max=*f*<sub>M</sub>+Δ*f*. That is, ask how long it takes for the different algorithms to obtain the minimum to within an absolute tolerance Δ*f*, for some Δ*f*. (This is *totally different* from using the ftol_abs termination test, because the latter uses only a crude estimate of the error in the function values, and moreover the estimate varies between algorithms.)
+
+Global optimization
+-------------------
+
+All of the global-optimization algorithms currently require you to specify bound constraints on all the optimization parameters. Of these algorithms, only ISRES and ORIG_DIRECT support nonlinear inequality constraints, and only ISRES supports nonlinear equality constraints. (However, any of them can be applied to nonlinearly constrained problems by combining them with the [augmented Lagrangian method](#Augmented_Lagrangian_algorithm.md) below.)
+
+**Something you should consider** is that, after running the global optimization, it is often worthwhile to then use the global optimum as a starting point for a local optimization to "polish" the optimum to a greater accuracy. (Many of the global optimization algorithms devote more effort to searching the global parameter space than in finding the precise position of the local optimum accurately.)
+
+### DIRECT and DIRECT-L
+
+DIRECT is the DIviding RECTangles algorithm for global optimization, described in:
+
+- D. R. Jones, C. D. Perttunen, and B. E. Stuckmann, "Lipschitzian optimization without the lipschitz constant," *J. Optimization Theory and Applications*, vol. 79, p. 157 (1993).
+
+and DIRECT-L is the "locally biased" variant proposed by:
+
+- J. M. Gablonsky and C. T. Kelley, "A locally-biased form of the DIRECT algorithm," *J. Global Optimization*, vol. 21 (1), p. 27-37 (2001).
+
+These is are deterministic-search algorithms based on systematic division of the search domain into smaller and smaller hyperrectangles. The Gablonsky version makes the algorithm "more biased towards local search" so that it is more efficient for functions without too many local minima. NLopt contains several implementations of both of these algorithms. I would tend to try `NLOPT_GN_DIRECT_L` first; YMMV.
+
+First, it contains a from-scratch re-implementation of both algorithms, specified by the constants `NLOPT_GN_DIRECT` and `NLOPT_GN_DIRECT_L`, respectively.
+
+Second, there is a slightly randomized variant of DIRECT-L, specified by `NLOPT_GN_DIRECT_L_RAND`, which uses some randomization to help decide which dimension to halve next in the case of near-ties.
+
+The DIRECT and DIRECT-L algorithms start by rescaling the bound constraints to a hypercube, which gives all dimensions equal weight in the search procedure. If your dimensions do *not* have equal weight, e.g. if you have a "long and skinny" search space and your function varies at about the same speed in all directions, it may be better to use unscaled variants of these algorthms, which are specified as `NLOPT_GNL_DIRECT_NOSCAL`, `NLOPT_GN_DIRECT_L_NOSCAL`, and `NLOPT_GN_DIRECT_L_RAND_NOSCAL`, respectively. However, the unscaled variations make the most sense (if any) with the original DIRECT algorithm, since the design of DIRECT-L to some extent relies on the search region being a hypercube (which causes the subdivided hyperrectangles to have only a small set of side lengths).
+
+Finally, NLopt also includes separate implementations based on the [original Fortran code](http://www4.ncsu.edu/~ctk/SOFTWARE/DIRECTv204.tar.gz) by Gablonsky et al. (1998-2001), which are specified as `NLOPT_GN_ORIG_DIRECT` and `NLOPT_GN_ORIG_DIRECT_L`. These implementations have a number of hard-coded limitations on things like the number of function evaluations; I removed several of these limitations, but some remain. On the other hand, there seem to be slight differences between these implementations and mine; most of the time, the performance is roughly similar, but occasionally Gablonsky's implementation will do significantly better than mine or vice versa.
+
+Most of the above algorithms only handle bound constraints, and in fact require finite bound constraints (they are not applicable to unconstrained problems). They do not handle arbitrary nonlinear constraints. However, the `ORIG` versions by Gablonsky et al. include some support for arbitrary nonlinear inequality constraints.
+
+### Controlled Random Search (CRS) with local mutation
+
+My implementation of the "controlled random search" (CRS) algorithm (in particular, the CRS2 variant) with the "local mutation" modification, as defined by:
+
+- P. Kaelo and M. M. Ali, "Some variants of the controlled random search algorithm for global optimization," *J. Optim. Theory Appl.* **130** (2), 253-264 (2006).
+
+The original CRS2 algorithm was described by:
+
+- W. L. Price, "A controlled random search procedure for global optimization," in *Towards Global Optimization 2*, p. 71-84 edited by L. C. W. Dixon and G. P. Szego (North-Holland Press, Amsterdam, 1978).
+
+<!-- -->
+
+- W. L. Price, "Global optimization by controlled random search," *J. Optim. Theory Appl.* **40** (3), p. 333-348 (1983).
+
+The CRS algorithms are sometimes compared to genetic algorithms, in that they start with a random "population" of points, and randomly "evolve" these points by heuristic rules. In this case, the "evolution" somewhat resembles a randomized Nelder-Mead algorithm. The published results for CRS seem to be largely empirical; limited analytical results about its convergence were derived in:
+
+- Eligius M. T. Hendrix, P. M. Ortigosa, and I. García, "On success rates for controlled random search," *J. Global Optim.* **21**, p. 239-263 (2001).
+
+The initial population size for CRS defaults to 10×(*n*+1) in *n* dimensions, but this can be changed with the [nlopt_set_population](NLopt_Reference#Stochastic_population.md) function; the initial population must be at least *n*+1.
+
+Only bound-constrained problems are supported by this algorithm.
+
+CRS2 with local mutation is specified in NLopt as `NLOPT_GN_CRS2_LM`.
+
+### MLSL (Multi-Level Single-Linkage)
+
+This is my implementation of the "Multi-Level Single-Linkage" (MLSL) algorithm for global optimization by a sequence of local optimizations from random starting points, proposed by:
+
+- A. H. G. Rinnooy Kan and G. T. Timmer, "Stochastic global optimization methods," *Mathematical Programming*, vol. 39, p. 27-78 (1987). (Actually 2 papers — part I: clustering methods, p. 27, then part II: multilevel methods, p. 57.)
+
+We also include a modification of MLSL use a Sobol' [low-discrepancy sequence](https://en.wikipedia.org/wiki/Low-discrepancy_sequence) (LDS) instead of pseudorandom numbers, which was argued to improve the convergence rate by:
+
+- Sergei Kucherenko and Yury Sytsko, "Application of deterministic low-discrepancy sequences in global optimization," *Computational Optimization and Applications*, vol. 30, p. 297-318 (2005).
+
+In either case, MLSL is a "multistart" algorithm: it works by doing a sequence of local optimizations (using some other local optimization algorithm) from random or low-discrepancy starting points. MLSL is distinguished, however by a "clustering" heuristic that helps it to avoid repeated searches of the same local optima, and has some theoretical guarantees of finding all local optima in a finite number of local minimizations.
+
+The local-search portion of MLSL can use any of the other algorithms in NLopt, and in particular can use either gradient-based (`D`) or derivative-free algorithms (`N`) The local search uses the derivative/nonderivative algorithm set by `nlopt_opt_set_local_optimizer`.
+
+LDS-based MLSL with is specified as `NLOPT_G_MLSL_LDS`, while the original non-LDS original MLSL (using pseudo-random numbers, currently via the [Mersenne twister](https://en.wikipedia.org/wiki/Mersenne_twister) algorithm) is indicated by `NLOPT_G_MLSL`. In both cases, you must specify the [local optimization](NLopt_Reference#Local/subsidiary_optimization_algorithm.md) algorithm (which can be gradient-based or derivative-free) via `nlopt_opt_set_local_optimizer`.
+
+**Note**: If you do not set a stopping tolerance for your local-optimization algorithm, MLSL defaults to ftol_rel=10<sup>−15</sup> and xtol_rel=10<sup>−7</sup> for the local searches. Note that it is perfectly reasonable to set a relatively large tolerance for these local searches, run MLSL, and then at the end run another local optimization with a lower tolerance, using the MLSL result as a starting point, to "polish off" the optimum to high precision.
+
+By default, each iteration of MLSL samples 4 random new trial points, but this can be changed with the [nlopt_set_population](NLopt_Reference#Stochastic_population.md) function.
+
+Only bound-constrained problems are supported by this algorithm.
+
+### StoGO
+
+This is an algorithm adapted from the code downloaded from
+
+- [StoGO global optimization library](http://www2.imm.dtu.dk/~km/GlobOpt/opt.html) (link broken as of Nov. 2009, and the software seems absent from the [author's web site](http://www2.imm.dtu.dk/~km/))
+
+by Madsen et al. StoGO is a global optimization algorithm that works by systematically dividing the search space (which must be bound-constrained) into smaller hyper-rectangles via a branch-and-bound technique, and searching them by a gradient-based local-search algorithm (a BFGS variant), optionally including some randomness (hence the "Sto", which stands for "stochastic" I believe).
+
+StoGO is written in C++, which means that it is only included when you compile the [C++ algorithms](NLopt_Installation.md) enabled, in which case (on Unix) you must link to `-lnlopt_cxx` instead of `-lnlopt`.
+
+StoGO is specified within NLopt by `NLOPT_GD_STOGO`, or `NLOPT_GD_STOGO_RAND` for the randomized variant.
+
+Some references on StoGO are:
+
+- S. Gudmundsson, "Parallel Global Optimization," M.Sc. Thesis, IMM, Technical University of Denmark, 1998.
+- K. Madsen, S. Zertchaninov, and A. Zilinskas, "Global Optimization using Branch-and-Bound," unpublished (1998). A preprint of this paper is included in the `stogo` subdirectory of NLopt as `paper.pdf`.
+- S. Zertchaninov and K. Madsen, "A C++ Programme for Global Optimization," IMM-REP-1998-04, Department of Mathematical Modelling, Technical University of Denmark, DK-2800 Lyngby, Denmark, 1998. A copy of this report is included in the `stogo` subdirectory of NLopt as `techreport.pdf`.
+
+Only bound-constrained problems are supported by this algorithm.
+
+### ISRES (Improved Stochastic Ranking Evolution Strategy)
+
+This is my implementation of the "Improved Stochastic Ranking Evolution Strategy" (ISRES) algorithm for nonlinearly-constrained global optimization (or at least semi-global; although it has heuristics to escape local optima, I'm not aware of a convergence proof), based on the method described in:
+
+- Thomas Philip Runarsson and Xin Yao, "[Search biases in constrained evolutionary optimization](http://www3.hi.is/~tpr/papers/RuYa05.pdf)," *IEEE Trans. on Systems, Man, and Cybernetics Part C: Applications and Reviews*, vol. 35 (no. 2), pp. 233-243 (2005).
+
+It is a refinement of an earlier method described in:
+
+- Thomas P. Runarsson and Xin Yao, "[Stochastic ranking for constrained evolutionary optimization](http://www3.hi.is/~tpr/software/sres/Tec311r.pdf)," *IEEE Trans. Evolutionary Computation*, vol. 4 (no. 3), pp. 284-294 (2000).
+
+This is an independent implementation by S. G. Johnson (2009) based on the papers above. Runarsson also has his own Matlab implemention available from his web page [here](http://www3.hi.is/~tpr).
+
+The evolution strategy is based on a combination of a mutation rule (with a log-normal step-size update and exponential smoothing) and differential variation (a Nelder–Mead-like update rule). The fitness ranking is simply via the objective function for problems without nonlinear constraints, but when nonlinear constraints are included the stochastic ranking proposed by Runarsson and Yao is employed. The population size for ISRES defaults to 20×(*n*+1) in *n* dimensions, but this can be changed with the [nlopt_set_population](NLopt_Reference#Stochastic_population.md) function.
+
+This method supports arbitrary nonlinear inequality and equality constraints in addition to the bound constraints, and is specified within NLopt as `NLOPT_GN_ISRES`.
+
+### ESCH (evolutionary algorithm)
+
+This is a modified Evolutionary Algorithm for global optimization, developed by Carlos Henrique da Silva Santos's and described in the following paper and Ph.D thesis:
+
+- C. H. da Silva Santos, M. S. Gonçalves, and H. E. Hernandez-Figueroa, "Designing Novel Photonic Devices by Bio-Inspired Computing," *IEEE Photonics Technology Letters* **22** (15), pp. 1177–1179 (2010).
+
+<!-- -->
+
+- C. H. da Silva Santos, "[Parallel and Bio-Inspired Computing Applied to Analyze Microwave and Photonic Metamaterial Strucutures](http://www.bibliotecadigital.unicamp.br/document/?code=000767537&opt=4&lg=en_US)," Ph.D. thesis, University of Campinas, (2010).
+
+The algorithm is adapted from ideas described in:
+
+- H.-G. Beyer and H.-P. Schwefel, "Evolution Strategies: A Comprehensive Introduction," *Journal Natural Computing*, **1** (1), pp. 3–52 (2002_.
+
+<!-- -->
+
+- Ingo Rechenberg, "Evolutionsstrategie – Optimierung technischer Systeme nach Prinzipien der biologischen Evolution," Ph.D. thesis (1971), Reprinted by Fromman-Holzboog (1973).
+
+The method supports bound constraints only (no nonlinear constraints), and is specified within NLopt as `NLOPT_GN_ESCH`.
+
+Local derivative-free optimization
+----------------------------------
+
+Of these algorithms, only COBYLA currently supports arbitrary nonlinear inequality and equality constraints; the rest of them support bound-constrained or unconstrained problems only. (However, any of them can be applied to nonlinearly constrained problems by combining them with the [augmented Lagrangian method](#Augmented_Lagrangian_algorithm.md) below.)
+
+### COBYLA (Constrained Optimization BY Linear Approximations)
+
+This is a derivative of Powell's implementation of the COBYLA (Constrained Optimization BY Linear Approximations) algorithm for derivative-free optimization with nonlinear inequality and equality constraints, by M. J. D. Powell, described in:
+
+- M. J. D. Powell, "A direct search optimization method that models the objective and constraint functions by linear interpolation," in *Advances in Optimization and Numerical Analysis*, eds. S. Gomez and J.-P. Hennart (Kluwer Academic: Dordrecht, 1994), p. 51-67.
+
+and reviewed in:
+
+- M. J. D. Powell, "Direct search algorithms for optimization calculations," *Acta Numerica* **7**, 287-336 (1998).
+
+It constructs successive linear approximations of the objective function and constraints via a simplex of *n*+1 points (in *n* dimensions), and optimizes these approximations in a trust region at each step.
+
+The original code itself was written in Fortran by Powell and was converted to C in 2004 by Jean-Sebastien Roy (js@jeannot.org) for the SciPy project. The version in NLopt was based on Roy's C version, downloaded from:
+
+- <http://www.jeannot.org/~js/code/index.en.html#COBYLA>
+
+NLopt's version is slightly modified in a few ways. First, we incorporated all of the NLopt termination criteria. Second, we added explicit support for bound constraints (although the original COBYLA could handle bound constraints as linear constraints, it would sometimes take a step that violated the bound constraints). Third, we allow `COBYLA` to increase the trust-region radius if the predicted improvement was approximately right and the simplex is OK, following a suggestion in the [SAS manual for PROC NLP](http://www.uc.edu/sashtml/iml/chap17/sect164.htm) that seems to improve convergence speed. Fourth, we pseudo-randomize simplex steps in COBYLA algorithm, improving robustness by avoiding accidentally taking steps that don't improve conditioning (which seems to happen sometimes with active bound constraints); the algorithm remains deterministic (a deterministic seed is used), however. Also, we support unequal initial-step sizes in the different parameters (by the simple expedient of internally rescaling the parameters proportional to the initial steps), which is important when different parameters have very different scales.
+
+(The underlying COBYLA code only supports inequality constraints. Equality constraints are automatically [transformed into pairs](NLopt_Introduction#Equality_constraints.md) of inequality constraints, which in the case of this algorithm seems not to cause problems.)
+
+It is specified within NLopt as `NLOPT_LN_COBYLA`.
+
+### BOBYQA
+
+This is an algorithm derived from the [BOBYQA subroutine](http://plato.asu.edu/ftp/other_software/bobyqa.zip) of M. J. D. Powell, converted to C and modified for the NLopt stopping criteria. BOBYQA performs derivative-free bound-constrained optimization using an iteratively constructed quadratic approximation for the objective function. See:
+
+- M. J. D. Powell, "[The BOBYQA algorithm for bound constrained optimization without derivatives](http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf)," Department of Applied Mathematics and Theoretical Physics, Cambridge England, technical report NA2009/06 (2009).
+
+(Because BOBYQA constructs a quadratic approximation of the objective, it may perform poorly for objective functions that are not twice-differentiable.)
+
+The NLopt BOBYQA interface supports unequal initial-step sizes in the different parameters (by the simple expedient of internally rescaling the parameters proportional to the initial steps), which is important when different parameters have very different scales.
+
+This algorithm, specified in NLopt as `NLOPT_LN_BOBYQA`, largely supersedes the NEWUOA algorithm below, which is an earlier version of the same idea by Powell.
+
+### NEWUOA + bound constraints
+
+This is an algorithm derived from the NEWUOA subroutine of M. J. D. Powell, converted to C and modified for the NLopt stopping criteria. I also modified the code to include a variant, NEWUOA-bound, that permits efficient handling of bound constraints. This algorithm is largely superseded by BOBYQA (above).
+
+The original NEWUOA performs derivative-free unconstrained optimization using an iteratively constructed quadratic approximation for the objective function. See:
+
+- M. J. D. Powell, "[The NEWUOA software for unconstrained optimization without derivatives](http://www.optimization-online.org/DB_HTML/2005/01/1045.html)," *Proc. 40th Workshop on Large Scale Nonlinear Optimization* (Erice, Italy, 2004).
+
+(Because NEWUOA constructs a quadratic approximation of the objective, it may perform poorly for objective functions that are not twice-differentiable.)
+
+The original algorithm is specified in NLopt as `NLOPT_LN_NEWUOA`, and only supports unconstrained problems. For bound constraints, my variant is specified as `NLOPT_LN_NEWUOA_BOUND`.
+
+In the original NEWUOA algorithm, Powell solved the quadratic subproblems (in routines TRSAPP and BIGLAG) in a spherical trust region via a truncated conjugate-gradient algorithm. In my bound-constrained variant, we use the MMA algorithm for these subproblems to solve them with both bound constraints and a spherical trust region. In principle, we should also change the BIGDEN subroutine in a similar way (since BIGDEN also approximately solves a trust-region subproblem), but instead I just truncated its result to the bounds (which probably gives suboptimal convergence, but BIGDEN is called only very rarely in practice).
+
+Shortly after my addition of bound constraints to NEWUOA, Powell released his own version of NEWUOA modified for bound constraints as well as some numerical-stability and convergence enhancements, called BOBYQA. NLopt now incorporates BOBYQA as well, and it seems to largely supersede NEWUOA.
+
+**Note:** NEWUOA requires the dimension *n* of the parameter space to be ≥ 2, i.e. the implementation does not handle one-dimensional optimization problems.
+
+### PRAXIS (PRincipal AXIS)
+
+"PRAXIS" gradient-free local optimization via the "principal-axis method" of Richard Brent, based on a C translation of Fortran code downloaded from [Netlib](https://en.wikipedia.org/wiki/Netlib):
+
+- <http://netlib.org/opt/praxis>
+
+The original Fortran code was written by Richard Brent and made available by the Stanford Linear Accelerator Center, dated 3/1/73. The appropriate reference seems to be:
+
+- Richard Brent, *Algorithms for Minimization without Derivatives* (Prentice-Hall, 1972). (Reprinted by Dover, 2002.)
+
+Specified in NLopt as `NLOPT_LN_PRAXIS`
+
+This algorithm was originally designed for unconstrained optimization. In NLopt, bound constraints are "implemented" in PRAXIS by the simple expedient of returning infinity (Inf) when the constraints are violated (this is done automatically—you don't have to do this in your own function). This seems to work, more-or-less, but appears to slow convergence significantly. If you have bound constraints, you are probably better off using COBYLA or BOBYQA.
+
+### Nelder-Mead Simplex
+
+My implementation of almost the original Nelder-Mead simplex algorithm (specified in NLopt as `NLOPT_LN_NELDERMEAD`), as described in:
+
+- J. A. Nelder and R. Mead, "A simplex method for function minimization," *The Computer Journal* **7**, p. 308-313 (1965).
+
+This method is simple and has demonstrated enduring popularity, despite the later discovery that it fails to converge at all for some functions (and examples may be constructed in which it converges to point that is not a local minimum). Anecdotal evidence suggests that it often performs well even for noisy and/or discontinuous objective functions. I would tend to recommend the Subplex method (below) instead, however.
+
+The main change compared to the 1965 paper is that I implemented explicit support for bound constraints, using essentially the method proposed in:
+
+- M. J. Box, "A new method of constrained optimization and a comparison with other methods," *Computer J.* **8** (1), 42-52 (1965).
+
+and later reviewed in:
+
+- J. A. Richardson and J. L. Kuester, "The complex method for constrained optimization," *Commun. ACM* **16** (8), 487-489 (1973).
+
+Whenever a new point would lie outside the bound constraints, Box advocates moving it "just inside" the constraints by some fixed "small" distance of 10<sup>−8</sup> or so. I couldn't see any advantage to using a fixed distance inside the constraints, especially if the optimum is on the constraint, so instead I move the point exactly onto the constraint in that case. The danger with implementing bound constraints in this way (or by Box's method) is that you may collapse the simplex into a lower-dimensional subspace. I'm not aware of a better way, however. In any case, this collapse of the simplex is somewhat ameliorated by restarting, such as when Nelder-Mead is used within the Subplex algorithm below.
+
+### Sbplx (based on Subplex)
+
+This is my re-implementation of Tom Rowan's "Subplex" algorithm. As Rowan expressed a preference that other implementations of his algorithm use a different name, I called my implementation "Sbplx" (referred to in NLopt as `NLOPT_LN_SBPLX`).
+
+Subplex (a variant of Nelder-Mead that uses Nelder-Mead on a sequence of subspaces) is claimed to be much more efficient and robust than the original Nelder-Mead, while retaining the latter's facility with discontinuous objectives, and in my experience these claims seem to be true in many cases. (However, I'm not aware of any proof that Subplex is globally convergent, and perhaps it may fail for some objectives like Nelder-Mead; YMMV.)
+
+I used the description of Rowan's algorithm in his PhD thesis:
+
+- T. Rowan, "Functional Stability Analysis of Numerical Algorithms", Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990.
+
+I would have preferred to use Rowan's original implementation, posted by him on Netlib:
+
+- <http://www.netlib.org/opt/subplex.tgz>
+
+Unfortunately, the legality of redistributing or modifying this code is unclear, because it lacks anything resembling a license statement. After some friendly emails with Rowan in which he promised to consider providing a clear open-source/free-software license, I lost touch with him and his old email address now seems invalid.
+
+Since the algorithm is not too complicated, however, I just rewrote it. There seem to be slight differences between the behavior of my implementation and his (probably due to different choices of initial subspace and other slight variations, where his paper was ambiguous), but the number of iterations to converge on my test problems seems to be quite close (within ±10% of the number of function evaluations for most problems).
+
+The only major difference between my implementation and Rowan's, as far as I can tell, is that I implemented explicit support for bound constraints (via the method in the Box paper as described above). This seems to be a big improvement in the case where the optimum lies against one of the constraints.
+
+Local gradient-based optimization
+---------------------------------
+
+Of these algorithms, only MMA and SLSQP support arbitrary nonlinear inequality constraints, and only SLSQP supports nonlinear equality constraints; the rest support bound-constrained or unconstrained problems only. (However, any of them can be applied to nonlinearly constrained problems by combining them with the [augmented Lagrangian method](#Augmented_Lagrangian_algorithm.md) below.)
+
+### MMA (Method of Moving Asymptotes) and CCSA
+
+My implementation of the globally-convergent method-of-moving-asymptotes (MMA) algorithm for gradient-based local optimization, including nonlinear inequality constraints (but *not* equality constraints), specified in NLopt as `NLOPT_LD_MMA`, as described in:
+
+- Krister Svanberg, "[A class of globally convergent optimization methods based on conservative convex separable approximations](http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.146.5196)," *SIAM J. Optim.* **12** (2), p. 555-573 (2002).
+
+This is an improved CCSA ("conservative convex separable approximation") variant of the original MMA algorithm published by Svanberg in 1987, which has become popular for topology optimization. (*Note:* "globally convergent" does *not* mean that this algorithm converges to the global optimum; it means that it is guaranteed to converge to *some* local minimum from any feasible starting point.)
+
+At each point **x**, MMA forms a local approximation using the gradient of *f* and the constraint functions, plus a quadratic "penalty" term to make the approximations "conservative" (upper bounds for the exact functions). The precise approximation MMA forms is difficult to describe in a few words, because it includes nonlinear terms consisting of a poles at some distance from *x* (outside of the current trust region), almost a kind of Pade approximant. The main point is that the approximation is both convex and separable, making it trivial to solve the approximate optimization by a dual method. Optimizing the approximation leads to a new candidate point **x**. The objective and constraints are evaluated at the candidate point. If the approximations were indeed conservative (upper bounds for the actual functions at the candidate point), then the process is restarted at the new **x**. Otherwise, the approximations are made more conservative (by increasing the penalty term) and re-optimized.
+
+(If you contact [Professor Svanberg](http://researchprojects.kth.se/index.php/kb_7902/pb_2085/pb.html), he has been willing in the past to graciously provide you with his original code, albeit under restrictions on commercial use or redistribution. The MMA implementation in NLopt, however, is completely independent of Svanberg's, whose code we have not examined; any bugs are my own, of course.)
+
+I also implemented another CCSA algorithm from the same paper, `NLOPT_LD_CCSAQ`: instead of constructing local MMA approximations, it constructs simple quadratic approximations (or rather, affine approximations plus a quadratic penalty term to stay conservative). This is the ccsa_quadratic code. It seems to have similar convergence rates to MMA for most problems, which is not surprising as they are both essentially similar. However, for the quadratic variant I implemented the possibility of [preconditioning](NLopt_Reference#Preconditioning_with_approximate_Hessians.md): including a user-supplied Hessian approximation in the local model. It is easy to incorporate this into the proof in Svanberg's paper, and to show that global convergence is still guaranteed as long as the user's "Hessian" is positive semidefinite, and it practice it can greatly improve convergence if the preconditioner is a good approximation for the real Hessian (at least for the eigenvectors of the largest eigenvalues).
+
+### SLSQP
+
+Specified in NLopt as `NLOPT_LD_SLSQP`, this is a sequential quadratic programming (SQP) algorithm for nonlinearly constrained gradient-based optimization (supporting both inequality and equality constraints), based on the implementation by Dieter Kraft and described in:
+
+- Dieter Kraft, "A software package for sequential quadratic programming", Technical Report DFVLR-FB 88-28, Institut für Dynamik der Flugsysteme, Oberpfaffenhofen, July 1988.
+- Dieter Kraft, "Algorithm 733: TOMP–Fortran modules for optimal control calculations," *ACM Transactions on Mathematical Software*, vol. 20, no. 3, pp. 262-281 (1994).
+
+(I believe that SLSQP stands for something like "Sequential Least-Squares Quadratic Programming," because the problem is treated as a sequence of constrained least-squares problems, but such a least-squares problem is equivalent to a QP.) The algorithm optimizes successive second-order (quadratic/least-squares) approximations of the objective function (via BFGS updates), with first-order (affine) approximations of the constraints.
+
+The Fortran code was obtained from the SciPy project, who are responsible for [obtaining permission](http://permalink.gmane.org/gmane.comp.python.scientific.devel/6725) to distribute it under a free-software (3-clause BSD) license.
+
+The code was modified for inclusion in NLopt by S. G. Johnson in 2010, with the following changes. The code was converted to C and manually cleaned up. It was modified to be re-entrant (preserving the reverse-communication interface but explicitly saving the state in a data structure). The reverse-communication interface was wrapped with an NLopt-style interface, with NLopt stopping conditions. The inexact line search was modified to evaluate the functions including gradients for the first step, since this removes the need to evaluate the function+gradient a second time for the same point in the common case when the inexact line search concludes after a single step; this is motivated by the fact that NLopt's interface combines the function and gradient computations. Since roundoff errors sometimes pushed SLSQP's parameters slightly outside the bound constraints (not allowed by NLopt), we added checks to force the parameters within the bounds. We fixed [a bug](http://projects.scipy.org/scipy/ticket/1231) in the LSEI subroutine (use of uninitialized variables) for the case where the number of equality constraints equals the dimension of the problem. The LSQ subroutine was modified to handle infinite lower/upper bounds (in which case those constraints are omitted).
+
+**Note:** Because the SLSQP code uses dense-matrix methods (ordinary BFGS, not low-storage BFGS), it requires *O*(*n*<sup>2</sup>) storage and *O*(*n*<sup>3</sup>) time in *n* dimensions, which makes it less practical for optimizing more than a few thousand parameters.
+
+### Low-storage BFGS
+
+This algorithm in NLopt (specified by NLOPT_LD_LBFGS), is based on a Fortran implementation of the low-storage BFGS algorithm written by Prof. Ladislav Luksan, and graciously posted online under the GNU LGPL at:
+
+- <http://www.uivt.cas.cz/~luksan/subroutines.html>
+
+The original L-BFGS algorithm, based on variable-metric updates via Strang recurrences, was described by the papers:
+
+- J. Nocedal, "Updating quasi-Newton matrices with limited storage," *Math. Comput.* **35**, 773-782 (1980).
+- D. C. Liu and J. Nocedal, "On the limited memory BFGS method for large scale optimization," ''Math. Programming' **45**, p. 503-528 (1989).
+
+I converted Prof. Luksan's code to C with the help of [f2c](https://en.wikipedia.org/wiki/f2c), and made a few minor modifications (mainly to include the NLopt termination criteria).
+
+One of the parameters of this algorithm is the number *M* of gradients to "remember" from previous optimization steps: increasing *M* increases the memory requirements but may speed convergence. NLopt sets *M* to a heuristic value by default, but this can be [changed by the set_vector_storage function](NLopt_Reference#Vector_storage_for_limited-memory_quasi-Newton_algorithms.md).
+
+### Preconditioned truncated Newton
+
+This algorithm in NLopt, is based on a Fortran implementation of a preconditioned inexact truncated Newton algorithm written by Prof. Ladislav Luksan, and graciously posted online under the GNU LGPL at:
+
+- <http://www.uivt.cas.cz/~luksan/subroutines.html>
+
+NLopt includes several variations of this algorithm by Prof. Luksan. First, a variant preconditioned by the low-storage BFGS algorithm with steepest-descent restarting, specified as `NLOPT_LD_TNEWTON_PRECOND_RESTART`. Second, simplified versions `NLOPT_LD_TNEWTON_PRECOND` (same without restarting), `NLOPT_LD_TNEWTON_RESTART` (same without preconditioning), and `NLOPT_LD_TNEWTON` (same without restarting or preconditioning).
+
+The algorithms are based on the ones described by:
+
+- R. S. Dembo and T. Steihaug, "Truncated Newton algorithms for large-scale optimization," *Math. Programming* **26**, p. 190-212 (1982).
+
+I converted Prof. Luksan's code to C with the help of [f2c](https://en.wikipedia.org/wiki/f2c), and made a few minor modifications (mainly to include the NLopt termination criteria).
+
+One of the parameters of this algorithm is the number *M* of gradients to "remember" from previous optimization steps: increasing *M* increases the memory requirements but may speed convergence. NLopt sets *M* to a heuristic value by default, but this can be [changed by the set_vector_storage function](NLopt_Reference#Vector_storage_for_limited-memory_quasi-Newton_algorithms.md).
+
+### Shifted limited-memory variable-metric
+
+This algorithm in NLopt, is based on a Fortran implementation of a shifted limited-memory variable-metric algorithm by Prof. Ladislav Luksan, and graciously posted online under the GNU LGPL at:
+
+- <http://www.uivt.cas.cz/~luksan/subroutines.html>
+
+There are two variations of this algorithm: `NLOPT_LD_VAR2`, using a rank-2 method, and `NLOPT_LD_VAR1`, using a rank-1 method.
+
+The algorithms are based on the ones described by:
+
+- J. Vlcek and L. Luksan, "Shifted limited-memory variable metric methods for large-scale unconstrained minimization," *J. Computational Appl. Math.* **186**, p. 365-390 (2006).
+
+I converted Prof. Luksan's code to C with the help of [f2c](https://en.wikipedia.org/wiki/f2c), and made a few minor modifications (mainly to include the NLopt termination criteria).
+
+One of the parameters of this algorithm is the number *M* of gradients to "remember" from previous optimization steps: increasing *M* increases the memory requirements but may speed convergence. NLopt sets *M* to a heuristic value by default, but this can be [changed by the set_vector_storage function](NLopt_Reference#Vector_storage_for_limited-memory_quasi-Newton_algorithms.md).
+
+Augmented Lagrangian algorithm
+------------------------------
+
+There is one algorithm in NLopt that fits into all of the above categories, depending on what subsidiary optimization algorithm is specified, and that is the augmented Lagrangian method described in:
+
+- Andrew R. Conn, Nicholas I. M. Gould, and Philippe L. Toint, "A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds," *SIAM J. Numer. Anal.* vol. 28, no. 2, p. 545-572 (1991).
+- E. G. Birgin and J. M. Martínez, "[Improving ultimate convergence of an augmented Lagrangian method](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.72.6121)," *Optimization Methods and Software* vol. 23, no. 2, p. 177-195 (2008).
+
+This method combines the objective function and the nonlinear inequality/equality constraints (if any) in to a single function: essentially, the objective plus a "penalty" for any violated constraints. This modified objective function is then passed to *another* optimization algorithm with *no* nonlinear constraints. If the constraints are violated by the solution of this sub-problem, then the size of the penalties is increased and the process is repeated; eventually, the process must converge to the desired solution (if it exists).
+
+The subsidiary optimization algorithm is specified by the `nlopt_set_local_optimizer` function, described in the [NLopt Reference](NLopt_Reference#Local/subsidiary_optimization_algorithm.md). (Don't forget to set a stopping tolerance for this subsidiary optimizer!) Since all of the actual optimization is performed in this subsidiary optimizer, the subsidiary algorithm that you specify determines whether the optimization is gradient-based or derivative-free. In fact, you can even specify a global optimization algorithm for the subsidiary optimizer, in order to perform global nonlinearly constrained optimization (although specifying a good stopping criterion for this subsidiary global optimizer is tricky).
+
+The augmented Lagrangian method is specified in NLopt as `NLOPT_AUGLAG`. We also provide a variant, `NLOPT_AUGLAG_EQ`, that only uses penalty functions for equality constraints, while inequality constraints are passed through to the subsidiary algorithm to be handled directly; in this case, the subsidiary algorithm must handle inequality constraints (e.g. MMA or COBYLA).
+
+While NLopt uses an independent re-implementation of the Birgin and Martínez algorithm, those authors provide their own free-software implementation of the method as part of the [TANGO](http://www.ime.usp.br/~egbirgin/tango/) project, and implementations can also be found in [semi-free](http://www.gnu.org/philosophy/categories.html#semi-freeSoftware) packages like [LANCELOT](http://www.numerical.rl.ac.uk/lancelot/blurb.html).
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt C-plus-plus Reference
+---
+
+NLopt is written in C and the C NLopt programming interface (API), as described in the [NLopt Reference](NLopt_Reference.md), is directly callable from C++.
+
+However, we also provide a C++ header file, nlopt.hpp, that wraps a more natural C++ interface around the NLopt API, which may be more convenient for C++ programmers. (This C++ API is also the basis for the NLopt wrappers in some other languages, such as [Python](NLopt_Python_Reference.md).)
+
+The main distinctions of the C++ API are:
+
+- Use of the `nlopt::` namespace.
+- Use of a bona-fide C++ `nlopt::opt` class, instead of `nlopt_opt`, with constructors, destructors, etcetera.
+- Use of `std::vector`<double> instead of array arguments.
+- Use of exceptions instead of returning error codes, and exception-safety in the objective/constraint functions.
+- Overloading and related C++ features to simplify some parts of the API.
+
+The main purpose of this section is to document the syntax and unique features of the C++ API; for more detail on the underlying features, please refer to the C documentation in the [NLopt Reference](NLopt_Reference.md).
+
+Compiling and linking your program to NLopt
+-------------------------------------------
+
+An NLopt program in C++ should include the NLopt C++ header file:
+
+`#include `<nlopt.hpp>
+
+On Unix, you would normally link your program exactly as for the C API, with a command something like:
+
+*`compiler`*` `*`...source/object` `files...`*` -lnlopt -lm -o myprogram`
+
+where *compiler* is `g++` or whatever is appropriate for your machine/system.
+
+The `nlopt::opt` object
+-----------------------
+
+The NLopt API revolves around an object of type `nlopt::opt`. Via methods of this object, all of the parameters of the optimization are specified (dimensions, algorithm, stopping criteria, constraints, objective function, etcetera), and then one finally calls the `nlopt::opt::optimize` method in order to perform the optimization. The object should normally be created via the constructor:
+
+```
+nlopt::opt(nlopt::algorithm, unsigned n);
+```
+
+
+given an `algorithm` (see [NLopt Algorithms](NLopt_Algorithms.md) for possible values) and the dimensionality of the problem (`n`, the number of optimization parameters). Whereas the C algorithms are specified by `nlopt_algorithm` constants of the form `NLOPT_MMA`, `NLOPT_COBYLA`, etcetera, the C++ `nlopt::algorithm` values are of the form `nlopt::MMA`, `nlopt::COBYLA`, etcetera (with the `NLOPT_` prefix replaced by the `nlopt::` namespace).
+
+There are also a copy constructor `nlopt::opt(nlopt::opt` `const&)` and an assignment `operator=(nlopt::opt` `const&)`, both of which make a copy of a given object (equivalent to `nlopt_copy` in the C API).
+
+If there is an error in the constructor (or copy constructor, or assignment), a `std::bad_alloc` exception is thrown.
+
+There is, of course, a `~nlopt::opt()` destructor, so the object will be automatically deallocated once it goes out of scope.
+
+The algorithm and dimension parameters of the object are immutable (cannot be changed without constructing a new object), but you can query them for a given object by the methods:
+
+```
+nlopt::algorithm nlopt::opt::get_algorithm() const;
+unsigned nlopt::opt::get_dimension() const;
+```
+
+
+You can get a (0-terminated) C-style string description of the algorithm via:
+
+```
+const char *nlopt::opt::get_algorithm_name() const;
+```
+
+
+(These accessor methods, along with the other methods below, will throw an exception if you use them on an object initialized with the default no-argument constructor, i.e. if you didn't specify an algorithm or dimensionality yet.)
+
+Objective function
+------------------
+
+The objective function is specified by calling one of the methods:
+
+```
+void nlopt::opt::set_min_objective(nlopt::vfunc f, void* f_data);
+void nlopt::opt::set_max_objective(nlopt::vfunc f, void* f_data);
+```
+
+
+depending on whether one wishes to minimize or maximize the objective function `f`, respectively. The function `f` should be of the form:
+
+```
+ double f(const std::vector`<double>` &x, std::vector`<double>` &grad, void* f_data);
+```
+
+
+The return value should be the value of the function at the point `x`, where `x` is a vector of length `n` of the optimization parameters (the same as the dimension passed to the constructor).
+
+In addition, if the argument `grad` is not empty $$i.e. `!grad.empty()` or equivalently `grad.size()>0`$$, then `grad` is a vector of length `n` which should (upon return) be set to the gradient of the function with respect to the optimization parameters at `x`. That is, `grad[i]` should upon return contain the partial derivative $\partial f / \partial x_i$, for $0 \leq i < n$, if `grad` is non-empty. Not all of the optimization algorithms (below) use the gradient information: for algorithms listed as "derivative-free," the `grad` argument will always be empty and need never be computed. (For algorithms that do use gradient information, however, `grad` may still be empty for some calls.)
+
+The `f_data` argument is the same as the one passed to `nlopt_set_min_objective` or `nlopt_set_max_objective`, and may be used to pass any additional data through to the function. (That is, it may be a pointer to some caller-defined data structure/type containing information your function needs, which you convert from `void*` by a typecast.) You can just pass `NULL` for `f_data` if you don't want to pass any additional information. Note that the `nlopt::opt` object does *not* make a copy of whatever is pointed to by your `f_data` pointer; you must not deallocate its contents until *after* you are done calling `nlopt::opt::optimize`. (There is a low-level way to make the nlopt::opt object "take ownership" of the f_data pointer, which is mainly used for wrapping other languages.)
+
+Technically, in order to use `std::vector`<double> arguments for your objective function, wrapping the C API which only uses `double*`, NLopt has to make a copy of the C `double*` array to convert it to `std::vector`<double>. This incurs a slight memory and time overhead, which is likely to be negligible in most applications, but can be avoided by instead passing a C-style objective function:
+
+```
+void nlopt::opt::set_min_objective(nlopt::func f, void* f_data);
+void nlopt::opt::set_max_objective(nlopt::func f, void* f_data);
+```
+
+
+where `f` is of the same form as the [C objective function](NLopt_Reference#Objective_function.md).
+
+Bound constraints
+-----------------
+
+The [bound constraints](NLopt_Reference#Bound_constraints.md) can be specified by calling the methods:
+
+```
+void nlopt::opt::set_lower_bounds(const std::vector`<double>` &lb);
+void nlopt::opt::set_upper_bounds(const std::vector`<double>` &ub);
+```
+
+
+where `lb` and `ub` are vectors of length *n* (the same as the dimension passed to the `nlopt::opt` constructor). For convenience, these are overloaded with functions that take a single number as arguments, in order to set the lower/upper bounds for all optimization parameters to a single constant:
+
+```
+void nlopt::opt::set_lower_bounds(double lb);
+void nlopt::opt::set_upper_bounds(double ub);
+```
+
+
+To retrieve the values of the lower/upper bounds, you can call one of:
+
+```
+void nlopt::opt::get_lower_bounds(std::vector`<double>` &lb);
+void nlopt::opt::get_upper_bounds(std::vector`<double>` &ub);
+std::vector`<double>` nlopt::opt::get_lower_bounds();
+std::vector`<double>` nlopt::opt::get_upper_bounds();
+```
+
+
+where the first two functions set their arguments (which must be vectors of length `n`) to copies of the bounds, and the second two functions return copies of the bounds as new vectors.
+
+Nonlinear constraints
+---------------------
+
+Just as for [nonlinear constraints in C](NLopt_Reference#Nonlinear_constraints.md), you can specify nonlinear inequality and equality constraints by the methods:
+
+```
+void nlopt::opt::add_inequality_constraint(nlopt::vfunc fc, void *fc_data, double tol=0);
+void nlopt::opt::add_equality_constraint(nlopt::vfunc h, void *h_data, double tol=0);
+```
+
+
+where the arguments `fc` and `h` have the same form as the objective function above. Just as for the objective function, these constraint functions can either take `std::vector`<double> arguments or can take double\* arguments exactly as in the C API.
+
+To remove all of the inequality and/or equality constraints from a given problem, you can call the following methods:
+
+```
+void nlopt::opt::remove_inequality_constraints();
+void nlopt::opt::remove_equality_constraints();
+```
+
+
+### Vector-valued constraints
+
+Just as for [nonlinear constraints in C](NLopt_Reference#Vector-valued_constraints.md), you can specify nonlinear inequality and equality constraints by the methods:
+
+```
+void nlopt::opt::add_inequality_mconstraint(nlopt::mfunc c, void *c_data, const vector`<double>` &tol);
+void nlopt::opt::add_equality_mconstraint(nlopt::mfunc c, void *c_data, const vector`<double>` &tol);
+```
+
+
+Here, `tol` is a vector of the tolerances in each constraint dimension; the dimensionality *m* of the constraint is determined by `tol.size()`. The constraint function `c` is of the same form as in C.
+
+(You can add multiple vector-valued constraints and/or scalar constraints in the same problem.)
+
+Stopping criteria
+-----------------
+
+As explained in the [C API Reference](NLopt_Reference#Stopping_criteria.md) and the [Introduction](NLopt_Introduction#Termination_conditions.md)), you have multiple options for different stopping criteria that you can specify. (Unspecified stopping criteria are disabled; i.e., they have innocuous defaults.)
+
+For each stopping criteria, there are (at least) two method: a `set` method to specify the stopping criterion, and a `get` method to retrieve the current value for that criterion. The meanings of each criterion are exactly the same as in the C API.
+
+```
+void nlopt::opt::set_stopval(double stopval);
+double nlopt::opt::get_stopval() const;
+```
+
+
+Stop when an objective value of at least stopval is found.
+
+```
+void nlopt::opt::set_ftol_rel(double tol);
+double nlopt::opt::get_ftol_rel() const;
+```
+
+
+Set relative tolerance on function value.
+
+```
+void nlopt::opt::set_ftol_abs(double tol);
+double nlopt::opt::get_ftol_abs() const;
+```
+
+
+Set absolute tolerance on function value.
+
+```
+void nlopt::opt::set_xtol_rel(double tol);
+double nlopt::opt::get_xtol_rel() const;
+```
+
+
+Set relative tolerance on optimization parameters.
+
+```
+void nlopt::opt::set_xtol_abs(const std::vector`<double>` &tol);
+void nlopt::opt::set_xtol_abs(double tol);
+void nlopt::opt::get_xtol_abs(std::vector`<double>` &tol) const;
+std::vector`<double>` nlopt::opt::get_xtol_abs() const;
+```
+
+
+Set absolute tolerances on optimization parameters. The `tol` vector must be of length `n` (the dimension specified in the `nlopt::opt` constructor). The second `set_xtol_abs` variant sets all `n` tolerances to the same value `tol`. The first `get_xtol_abs` variant modifies its argument to a copy of the current tolerances, whereas the second variant returns a copy.
+
+```
+void nlopt::opt::set_maxeval(int maxeval);
+int nlopt::opt::get_maxeval() const;
+```
+
+
+Stop when the number of function evaluations exceeds `maxeval`.
+
+```
+void nlopt::opt::set_maxtime(double maxtime);
+double nlopt::opt::get_maxtime() const;
+```
+
+
+Stop when the optimization time (in seconds) exceeds `maxtime`.
+
+### Forced termination
+
+In certain cases, the caller may wish to *force* the optimization to halt, for some reason unknown to NLopt. For example, if the user presses Ctrl-C, or there is an error of some sort in the objective function. You can do this by throwing *any* exception inside your objective/constraint functions: the exception will be caught, the optimization will be halted gracefully, and another exception (possibly not the same one) will be rethrown. See [Exceptions](#Exceptions.md), below. The C++ equivalent of `nlopt_forced_stop` from the [C API](NLopt_Reference#Forced_termination.md) is to throw an `nlopt::forced_stop` exception.
+
+Performing the optimization
+---------------------------
+
+Once all of the desired optimization parameters have been specified in a given object `opt`, you can perform the optimization by calling:
+
+```
+nlopt::result nlopt::opt::optimize(std::vector`<double>` &x, double &opt_f);
+```
+
+
+On input, `x` is a vector of length `n` (the dimension of the problem from the `nlopt::opt` constructor) giving an initial guess for the optimization parameters. On successful return, `x` contains the optimized values of the optimization parameters, and `opt_f` contains the corresponding value of the objective function.
+
+The return value (see below) is positive on success, indicating the reason for termination. On failure (negative return codes), it throws an exception (see [Exceptions](#Exceptions.md), below).
+
+You can also call the following methods to retrieve the `opt_f` value from the last `optimize` call, and the return value (including negative/failure return values) from the last `optimize` call:
+
+```
+double nlopt::opt::last_optimum_value() const;
+nlopt::result nlopt::opt::last_optimize_result() const;
+```
+
+
+### Return values
+
+The possible return values are the same as the [return values in the C API](NLopt_Reference#Return_values.md), except that the `NLOPT_` prefix is replaced with the `nlopt::` namespace. That is, `NLOPT_SUCCESS` becomes `nlopt::SUCCESS`, etcetera.
+
+Exceptions
+----------
+
+The [Error codes (negative return values)](NLopt_Reference#Error_codes_(negative_return_values).md) in the C API are replaced in the C++ API by thrown exceptions. The following exceptions are thrown by the various routines:
+
+```
+std::runtime_error
+```
+
+Generic failure, equivalent to `NLOPT_FAILURE`.
+
+```
+std::invalid_argument
+```
+
+Invalid arguments (e.g. lower bounds are bigger than upper bounds, an unknown algorithm was specified, etcetera), equivalent to `NLOPT_INVALID_ARGS`.
+
+```
+std::bad_alloc
+```
+
+Ran out of memory (a memory allocation failed), equivalent to `NLOPT_OUT_OF_MEMORY`.
+
+`nlopt::roundoff_limited` (subclass of `std::runtime_error`)
+Halted because roundoff errors limited progress, equivalent to `NLOPT_ROUNDOFF_LIMITED`.
+
+`nlopt::forced_stop` (subclass of `std::runtime_error`)
+Halted because of a [forced termination](#Forced_termination.md): the user called `nlopt::opt::force_stop()` from the user’s objective function or threw an `nlopt::forced_stop` exception. Equivalent to `NLOPT_FORCED_STOP`.
+
+If your objective/constraint functions throw *any* exception during the execution of `nlopt::opt::optimize`, it will be caught by NLopt and the optimization will be halted gracefully, and `nlopt::opt::optimize` will re-throw an exception. However, the exception that is re-thrown by `nlopt::opt::optimize` will be one of the five exceptions above; if the exception thrown by your code was not one of these five, it will be converted to a generic `std::runtime_error` exception. (The reason for this is that C++ has no clean way to save an arbitrary exception and rethrow it later, outside the original `catch` statement.) Therefore, if you want to do something special in response to a particular exception that is not one of these five, you should catch it yourself in your function, handle it however you want, and re-throw if desired.
+
+Local/subsidiary optimization algorithm
+---------------------------------------
+
+Some of the algorithms, especially MLSL and AUGLAG, use a different optimization algorithm as a subroutine, typically for local optimization. You can change the local search algorithm and its tolerances by calling:
+
+```
+void nlopt::opt::set_local_optimizer(const nlopt::opt &local_opt);
+```
+
+
+Here, `local_opt` is another `nlopt::opt` object whose parameters are used to determine the local search algorithm, its stopping criteria, and other algorithm parameters. (However, the objective function, bounds, and nonlinear-constraint parameters of `local_opt` are ignored.) The dimension `n` of `local_opt` must match that of `opt`.
+
+This function makes a copy of the `local_opt` object, so you can freely destroy your original `local_opt` afterwards.
+
+Initial step size
+-----------------
+
+Just as in the C API, you can [get and set the initial step sizes](NLopt_Reference#Initial_step_size.md) for derivative-free optimization algorithms. The C++ equivalents of the C functions are the following methods:
+
+```
+void nlopt::opt::set_initial_step(const std::vector`<double>` &dx);
+void nlopt::opt::set_initial_step(double dx);
+void nlopt::opt::get_initial_step(const std::vector`<double>` &x, std::vector`<double>` &dx) const;
+std::vector`<double>` nlopt::opt::get_initial_step(const std::vector`<double>` &x) const;
+```
+
+
+Stochastic population
+---------------------
+
+Just as in the C API, you can [get and set the initial population](NLopt_Reference#Stochastic_population.md) for stochastic optimization algorithms, by the methods:
+
+```
+void nlopt::opt::set_population(unsigned pop);
+unsigned nlopt::opt::get_population() const;
+```
+
+
+(A `pop` of zero implies that the heuristic default will be used.)
+
+Pseudorandom numbers
+--------------------
+
+For stochastic optimization algorithms, we use pseudorandom numbers generated by the [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_twister) algorithm, based on code from Makoto Matsumoto. By default, the [seed](https://en.wikipedia.org/wiki/Random_seed) for the random numbers is generated from the system time, so that you will get a different sequence of pseudorandom numbers each time you run your program. If you want to use a "deterministic" sequence of pseudorandom numbers, i.e. the same sequence from run to run, you can set the seed by calling:
+
+```
+void nlopt::srand(unsigned long seed);
+```
+
+
+To reset the seed based on the system time, you can call:
+
+```
+void nlopt::srand_time();
+```
+
+
+(Normally, you don't need to call this as it is called automatically. However, it might be useful if you want to "re-randomize" the pseudorandom numbers after calling `nlopt::srand` to set a deterministic seed.)
+
+Vector storage for limited-memory quasi-Newton algorithms
+---------------------------------------------------------
+
+Just as in the C API, you can get and set the [number *M* of stored vectors](NLopt_Reference#Vector_storage_for_limited-memory_quasi-Newton_algorithms.md) for limited-memory quasi-Newton algorithms, via the methods:
+
+```
+void nlopt::opt::set_vector_storage(unsigned M);
+unsigned nlopt::opt::get_vector_storage() const;
+```
+
+
+(The default is *M*=0, in which case NLopt uses a heuristic nonzero value.)
+
+Version number
+--------------
+
+To determine the version number of NLopt at runtime, you can call:
+
+```
+void nlopt::version(int &major, int &minor, int &bugfix);
+```
+
+
+For example, NLopt version 3.1.4 would return `major=3`, `minor=1`, and `bugfix=4`. You can also retrieve these three values individually by calling:
+
+```
+int nlopt::version_major();
+int nlopt::version_minor();
+int nlopt::version_bugfix();
+```
+
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt Deprecated API Reference
+---
+
+NLopt is a library, not a stand-alone program—it is designed to be called from your own program in C, C++, Fortran, Matlab, GNU Octave, or other languages. This reference section describes the original programming interface (API) of NLopt, used in versions of NLopt prior to 2.0. This interface is still supported in NLopt 2.0 (and will continue to be supported indefinitely if possible), for backwards compatibility, but is now deprecated in favor of the new object-style API in the [NLopt Reference](NLopt_Reference.md).
+
+The reason why this API is deprecated is that it is not easily extensible. A single optimization function was appropriate when NLopt started out as a library just handling bound constraints, but as more and more optimization parameters were added it became difficult to do this in a backwards-compatible way. (Also, functions with dozens of parameters at some point become unreadable.)
+
+Other sources of information include the Unix [man pages](https://en.wikipedia.org/wiki/Manual_page_(Unix)) for the functions. On Unix, you can run e.g. `man` `nlopt_minimize` for documentation of the `nlopt_minimize` function. In Matlab and GNU Octave, the corresponding command is to type `help` `nlopt_minimize`.
+
+Linking your program to NLopt
+-----------------------------
+
+For programs in compiled languages like C or Fortran, when you compile your program you will have to link it to the NLopt library. This is *in addition* to including the header file (`#include` <nlopt.h> in C/C++). On Unix, you would normally link with a command something like:
+
+*`compiler`*` `*`...source/object` `files...`*` -lnlopt -lm -o myprogram`
+
+where *compiler* is `cc`, `f77`, `g++`, or whatever is appropriate for your machine/language.
+
+*Note:* the `-lnlopt` `-lm` options, which link to the NLopt library (and the math library, which it requires), must come *after* your source/object files. In general, the rule is that if *A* depends upon *B*, then *A* must come before *B* in the link command.
+
+*Note:* the above example assumes that you have installed the NLopt library in a place where the compiler knows to find it (e.g. in a standard directory like `/usr/lib` or `/usr/local/lib`). If you installed somewhere else (e.g. in your home directory if you are not a system administrator), then you will need to use a `-L` flag to tell the compiler where to find the library. See [the installation manual](NLopt_Installation#Changing_the_installation_directory.md).
+
+C/C++ programming interface
+---------------------------
+
+To use NLopt from C or C++, you should first include the NLopt header file:
+
+`#include `<nlopt.h>
+
+Then, you should write functions to express your objective and constraints. Finally, you should call the function `nlopt_minimize_constrained` (for nonlinearly constrained optimization) or `nlopt_minimize` (for unconstrained or box-constrained optimization) to perform the optimization. There are also a couple of other utility routines described below.
+
+### `nlopt_minimize_constrained`
+
+```
+nlopt_result nlopt_minimize_constrained(nlopt_algorithm algorithm,
+ int n,
+ nlopt_func f, void* f_data,
+ int m,
+ nlopt_func fc, void* fc_data, ptrdiff_t fc_datum_size,
+ const double* lb, const double* ub,
+ double* x,
+ double* minf,
+ double minf_max,
+ double ftol_rel, double ftol_abs,
+ double xtol_rel, const double* xtol_abs,
+ int maxeval, double maxtime);
+```
+
+
+This function attempts to minimize a nonlinear function `f` of `n` optimization parameters, subject to `m` nonlinear constraints described by the function `fc`, using the specified algorithm. The minimum function value found is returned in `minf`, with the corresponding optimization parameter values returned in the array `x` of length `n`. The input values in `x` should be a starting guess for the minimum. The inputs `lb` and `ub` are arrays of length `n` containing lower and upper bounds, respectively, on the design variables `x`. The other parameters specify termination criteria (tolerances, the maximum number of function evaluations, etcetera) and other information described in more detail below. The return value is an integer code indicating success (positive) or failure (negative), as described below.
+
+#### Parameters
+
+The parameters specifying the optimization problem are:
+
+- `algorithm` — which optimization algorithm to use; its values are one of a set of predefined constants like`NLOPT_LD_MMA`, `NLOPT_GN_DIRECT`, etcetera, as described on the [NLopt Algorithms](NLopt_Algorithms.md) page.
+- `n` — the dimension *n* ≥ 0 of the optimization problem, the number of optimization parameters.
+- `f` — the objective function (see below)
+- `f_data` — a pointer to any data you want to pass to the the objective function (see below)
+- `m` — the number of nonlinear inequality constraints (zero for no such constraints).
+- `fc` — the nonlinear inequality constraint function (see below). Ignored if `m` = 0.
+- `fc_data`, `fc_datum_size` — `fc_data` is a pointer to an array of data to pass to the constraint function `fc`. The array should of length `m`, and each element of the array should have size `fc_datum_size` bytes. (See below for more information on constraint functions.) Ignored if `m` = 0.
+- `lb` — pointer to an array of length `n` of lower bounds on each optimization variable. That is, the optimization variables are constrained to have `x[i]` ≥ `lb[i]`. If you don't want a particular variable to be bounded below, just set the corresponding `lb[i]` to be `-HUGE_VAL`. (`HUGE_VAL` is a standard C constant, usually giving +∞.)
+- `ub` — pointer to an array of length `n` of upper bounds on each optimization variable. That is, the optimization variables are constrained to have `x[i]` ≤ `ub[i]`. If you don't want a particular variable to be bounded above, just set the corresponding `ub[i]` to be `+HUGE_VAL`.
+
+Starting guess and returned optimum:
+
+- `x` — an array of length `n` of the optimization parameters `x[0]`, ..., `x[n-1]`. On input, a starting guess for the optimum parameters; on output, the best found values of the parameters. (For a *local* optimization routine, the starting guess `x` determines which local optimum is found.) The starting guess is required to satisfy the bound constraints `lb` and `ub`; it need not satisfy the nonlinear inequality constraints `fc` (although it might be more efficient if you have a feasible starting guess.)
+- `minf` — on output, the minimum value of the objective function that was found (corresponding to the output value of the parameters `x`).
+
+The remaining parameters specify the termination conditions. Please read the [introduction to the termination conditions](NLopt_Introduction#Termination_conditions.md) for a general overview of these criteria. (In particular, note that you do *not* need to use *all* of these conditions; typically, you will use only one or two, and set the remainder to innocuous values.)
+
+- `minf_max` — stop if the objective function value drops below `minf_max`. (Set to `-HUGE_VAL` to ignore.)
+- `ftol_rel`, `ftol_abs` — relative and absolute tolerances in the objective function value. (Set to zero to ignore.)
+- `xtol_rel`, `xtol_abs` — relative and absolute tolerances in the optimization parameter values. `xtol_abs` should either be `NULL`, in which case it is ignored (equivalent to zero tolerance), or otherwise it should point to an array of length `n` containing absolute tolerances in each parameter `x[i]`. Set any tolerance to zero for it to be ignored.
+- `maxeval` — stop if the objective function is evaluated at least `maxeval` times. Set to zero to ignore.
+- `maxtime` — stop if the elapsed wall-clock time, in seconds, exceeds `maxtime`. Set to zero to ignore.
+
+#### Return value
+
+The value returned is one of the following enumerated constants.
+
+Successful termination (positive return values):
+
+- `NLOPT_SUCCESS` (= +1) — Generic success return value.
+- `NLOPT_MINF_MAX_REACHED` (= +2) — Optimization stopped because `minf_max` (above) was reached.
+- `NLOPT_FTOL_REACHED` (= +3) — Optimization stopped because `ftol_rel` or `ftol_abs` (above) was reached.
+- `NLOPT_XTOL_REACHED` (= +4) — Optimization stopped because `xtol_rel` or `xtol_abs` (above) was reached.
+- `NLOPT_MAXEVAL_REACHED` (= +5) — Optimization stopped because `maxeval` (above) was reached.
+- `NLOPT_MAXTIME_REACHED` (= +6) — Optimization stopped because `maxtime` (above) was reached.
+
+Error codes (negative return values):
+
+- `NLOPT_FAILURE` (= −1) — Generic failure code.
+- `NLOPT_INVALID_ARGS` (= −2) — Invalid arguments (e.g. lower bounds are bigger than upper bounds, an unknown algorithm was specified, etcetera).
+- `NLOPT_OUT_OF_MEMORY` (= −3) — Ran out of memory.
+- `NLOPT_ROUNDOFF_LIMITED` (= −4) — Roundoff errors led to a breakdown of the optimization algorithm. In this case, the returned minimum may still be useful. (e.g. this error occurs in NEWUOA if one tries to achieve a tolerance too close to machine precision.)
+
+### `nlopt_minimize`
+
+```
+nlopt_result nlopt_minimize(nlopt_algorithm algorithm,
+ int n,
+ nlopt_func f, void* f_data,
+ const double* lb, const double* ub,
+ double* x,
+ double* minf,
+ double minf_max,
+ double ftol_rel, double ftol_abs,
+ double xtol_rel, const double* xtol_abs,
+ int maxeval, double maxtime);
+```
+
+
+This function is exactly equivalent to calling `nlopt_minimize_constrained` with `m` = 0. That is, this is minimization with no nonlinear inequality constraints (although there may still be bound constraints `lb` and `ub`).
+
+### Objective function
+
+You should define your objective function (the function you want to minimize) as a function of the following form:
+
+```
+double f(int n, const double *x, double *grad, void *f_data)
+{
+ ....
+}
+```
+
+
+The return value should be the value of the function at the point **x**, where `x` points to an array of length `n` containing the optimization parameters. (That is, the optimization parameters are `x[0]`, `x[1]`, ..., `x[n-1]`.) The dimension `n` is the same as the one passed to `nlopt_minimize` or `nlopt_minimize_constrained`.
+
+In addition, if the argument `grad` is not `NULL`, then `grad` points to an array of length `n` that should (upon return) be set to the gradient of your function *f* with respect to the design variables *x*. That is, `grad[i]` should upon return contain the partial derivative ∂`f`/∂`x[i]`, for `i`=0,...,`n-1`. Not all of the [optimization algorithms](NLopt_Algorithms.md) use the gradient information: for algorithms listed as "derivative-free," the `grad` argument will always be `NULL` and need never be computed. (For algorithms that do use gradient information, however, `grad` may still be `NULL` for some calls.)
+
+The `f_data` argument is the same as the one passed to `nlopt_minimize` or `nlopt_minimize_constrained`, and may be used to pass any additional data through to the function. (That is, it may be a pointer to some caller-defined data structure/type containing information your function needs, which you convert from `void*` by a typecast.)
+
+### Nonlinear constraints
+
+The `nlopt_minimize_constrained` function allows you to specify `m` nonlinear constraints via the function `fc`, where `m` is any nonnegative integer. However, nonzero `m` is currently only supported by the `NLOPT_LD_MMA` and `NLOPT_LN_COBYLA` [algorithms](NLopt_Algorithms.md).
+
+In particular, the nonlinear constraints are of the form *fc*(*x*) ≤ 0, where the function fc is of the same form as the objective function described above:
+
+```
+double fc(int n, const double* x, double* grad, void* fc_datum);
+```
+
+
+The return value should be the value of the constraint function at the point `x` (an array of length `n`), where the dimension `n` is identical to the one passed to `nlopt_minimize_constrained`. As for the objective function, if the argument `grad` is not `NULL`, then `grad` points to an array of length `n` which should (upon return) be set to the gradient of the constraint function with respect to **x**. (For any algorithm listed as "derivative-free", the `grad` argument will always be `NULL` and need never be computed.)
+
+The `fc_datum` argument is based on the `fc_data` argument passed to `nlopt_minimize_constrained`, and may be used to pass any additional data through to the function, and is used to distinguish between different constraints.
+
+In particular, the constraint function `fc` will be called (at most) `m` times for each `x`, and the *i*-th constraint (0 ≤ *i* < *m*) will be passed an `fc_datum` argument equal to `fc_data` offset by *i*⋅`fc_datum_size`. For example, suppose that you have a data structure of type `foo` that describes the data needed by each constraint, and you store the information for the constraints in an array `foo` `data[m]`. In this case, you would pass `data` as the `fc_data` parameter to `nlopt_minimize_constrained`, and `sizeof(foo)` as the `fc_datum_size` parameter. Then, your `fc` function would be called `m` times for each point, and be passed `&data[0]` through `&data[m-1]` in sequence.
+
+### Mixed global/local search algorithm
+
+Some of the [global optimization algorithms](NLopt_Algorithms#Global_optimization.md) (currently, only MLSL) combine some global search scheme with a separate local optimization algorithm for local searches. For example, MLSL performs a sequence of local searches from semi-random starting points.
+
+Using the following functions, you can control *which* local search algorithm is used for MLSL (and any similar algorithm that is added in the future), as well as specifying a maximum number of function evaluations for the local search:
+
+```
+void nlopt_set_local_search_algorithm(nlopt_algorithm deriv, nlopt_algorithm nonderiv, int maxeval);
+```
+
+
+Set the local gradient-based search algorithm to `deriv` (default is `NLOPT_LD_MMA`), the local derivative-free search algorithm to `nonderiv` (default is `NLOPT_LN_COBYLA`), and the maximum number of function evaluations on each local search to `maxeval` (default is `-1`, for no maximum). Conversely, you can get the current values of these parameters by calling:
+
+```
+void nlopt_get_local_search_algorithm(nlopt_algorithm *deriv, nlopt_algorithm *nonderiv, int *maxeval)
+```
+
+
+*Note:* these parameters have no effect on local searches that you perform yourself; they are *only* for local searches that are performed *within* another algorithm like MLSL.
+
+### Population size for stochastic algorithms
+
+Stochastic (randomized) optimization algorithms are often parameterized by some initial "population" size (a set of sample points where the function is evaluated). NLopt tries to pick a reasonable default value for these population sizes, but in some cases the use may want finer control. This is achieved by the following two functions:
+
+```
+void nlopt_set_stochastic_population(int pop);
+int nlopt_get_stochastic_population(void);
+```
+
+
+which set and get the current (global) setting of the population parameter for stochastic algorithms. The default value of this population parameter is *zero*: a zero population is specially interpreted to mean that the algorithm should choose an algorithm-specific default value. These algorithm-specific defaults are documented with the [algorithms](NLopt_Algorithms.md) that use the population parameter.
+
+Fortran programming interface
+-----------------------------
+
+NLopt is callable from Fortran 77 (and later Fortran dialects), via special Fortran-callable wrapper subroutines that are included in the NLopt library.
+
+Although the functionality is the same as that of the C routines, the Fortran routines have different names and the arguments are passed in slightly different ways, as explained below.
+
+The most noticeable difference is that all function return values in C are changed into the first argument in Fortran, because there is no portable way to call C functions that return a value from Fortran or vice versa. The other noticeable difference is that, because there is no (portable) way to pass `NULL` in Fortran, any C argument that can optionally be `NULL` is converted to two arguments in Fortran, where the second argument is a flag to say whether that argument should be treated as `NULL` (i.e., ignored).
+
+### Constants and include files
+
+In C/C++, the `nlopt.h` header file declares the various constants (`NLOPT_LN_NELDERMEAD`, `NLOPT_FAILURE`, etcetera) used to specify the optimization algorithm, return codes, and so forth. In Fortran, the corresponding definitions are located in the `nlopt.f` file, which is installed into the same directory as `nlopt.h` (in `/usr/local/include` by default).
+
+That is, in any Fortran subroutine where you want to use NLopt subroutines, you should do:
+
+```
+include 'nlopt.f'
+```
+
+
+to include the constant definitions. (Like in C, most Fortran compilers allow you to pass `-I` options to specify search directories for include files, if you did not install NLopt in a standard location; see the [installation instructions](NLopt_Installation.md).) If you have some ancient Fortran compiler that does not support the `include` directive (which technically was nonstandard until Fortran 90, although most Fortran 77 compilers implement it), then I suppose you could also copy-and-paste the `nlopt.f` file directly into your source code.
+
+### `nloptc`
+
+The Fortran analogue to the `nlopt_minimize_constrained` function is:
+
+```
+call nloptc(info, algorithm, n,
+ f, f_data,
+ m, fc, fc_data, fc_second_datum,
+ lb, ub,
+ x, minf,
+ minf_max, ftol_rel, ftol_abs, xtol_rel, xtol_abs, have_xtol_abs, maxeval, maxtime)
+```
+
+
+The parameters are similar to those of `nlopt_minimize_constrained` (see also the documentation above):
+
+- `info` (integer, OUT) — on output, the return value, positive on success and negative on failure (see above for the specific return codes `NLOPT_SUCCESS` etcetera).
+
+<!-- -->
+
+- `algorithm` (integer, IN) — integer constant (`NLOPT_LN_NELDERMEAD`, etcetera) indicating the optimization algorithm to use (defined in `nlopt.f` include file as described above)
+- `n` (integer, IN) — the dimension of the problem (the number of optimization parameters, as in C)
+- `f` (subroutine, IN) — the objective function, actually a subroutine as described below
+- `f_data` (any type, IN) — any additional data to pass to the objective function
+- `m` (integer, IN) — the number of nonlinear inequality constraints (zero if none).
+- `fc` (subroutine, IN) — the constraint subroutine, as described below (ignored if *m*=0)
+- `fc_data`, `fc_second_datum` (arbitrary types, IN) — data to pass to the constraint subroutine, as described below (ignored if *m*=0)
+- `lb` (double precision array(`n`), IN) — lower bounds on the optimization parameters. (For unbounded dimensions, use `-Infinity` or `-Inf` in the Fortran 2003 standard; I don't know of a standard way to do it in earlier Fortran versions, maybe `-1.0/0.0`?)
+- `ub` (double precision array(`n`), IN) — upper bounds on the optimization parameters. (For unbounded dimensions, use `+Infinity` or `+Inf` in the Fortran 2003 standard; I don't know of a standard way to do it in earlier Fortran versions, maybe `+1.0/0.0`?)
+
+<!-- -->
+
+- `x` (double precision array(`n`), IN/OUT) — on input, an initial guess for the optimization parameters; on output, the best parameters found
+- `minf` (double precision, OUT) — on output, the minimum value of the objective function that was found
+
+Termination conditions (see [introduction](NLopt_Introduction#Termination_conditions.md)):
+
+- `minf_max` (double precision, IN) — stop if the an objective function value ≤ `minf_max` is found (set to `-Infinity`, or a huge negative number, to ignore).
+- `ftol_rel`, `ftol_abs` (double precision, IN) — relative and absolute tolerances in the objective function value (ignored if zero).
+- `xtol_rel` (double precision, IN) — relative tolerance in the optimization parameters (ignored if zero)
+- `xtol_abs` (double precision array(`n`), IN) — if `have_xtol_abs` is nonzero, then `xtol_abs` is an array of the absolute tolerances in each optimization parameter (ignored if zero).
+- `have_xtol_abs` (integer, IN) — if zero, then `xtol_abs` is ignored
+- `maxeval` (integer, IN) — stop if the objective function is evaluated at least `maxeval` times (set to zero to ignore)
+- `maxtime` (double precision, IN) — stop if the elapsed wall-clock time exceeds `maxtime` seconds (set to zero to ignore)
+
+### `nloptm`
+
+The Fortran analogue to the `nlopt_minimize` function is:
+
+```
+call nloptm(info, algorithm, n,
+ f, f_data,
+ lb, ub,
+ x, minf,
+ minf_max, ftol_rel, ftol_abs, xtol_rel, xtol_abs, have_xtol_abs, maxeval, maxtime)
+```
+
+
+This is exactly equivalent to calling `nloptc` with `m`=0.
+
+### Objective function in Fortran
+
+You should define your objective function (the function you want to minimize) as a subroutine of the following form:
+
+```
+subroutine f(val, n, x, grad, need_gradient, f_data)
+double precision val
+integer n
+double precision x(n)
+double precision grad(n)
+integer need_gradient
+```
+
+
+The `n`, `x`, `need_gradient`, and `f_data` parameters are inputs, and the `val` and `grad` parameters are outputs.
+
+Upon return, `val` should be set to the value of your objective function at the point **x**. The dimension `n` is the same as the one passed to `nloptm` or `nloptc`.
+
+In addition, if the argument `need_gradient` is not zero, then `grad` is an array of length `n` that should (upon return) be set to the gradient of your function *f* with respect to the design variables *x*. That is, `grad(i)` should upon return contain the partial derivative ∂`f`/∂`x(i)`, for `i`=1,...,`n`. Not all of the [optimization algorithms](NLopt_Algorithms.md) use the gradient information: for algorithms listed as "derivative-free," the `need_gradient` argument will always be zero and need never be computed. (For algorithms that do use gradient information, however, `need_gradient` may still be zero for some calls.) You should *not* access the `grad` array *at all* if `need_gradient` is zero.
+
+The `f_data` argument is the same as the one passed to `nloptm` or `nloptc`, and may be used to pass any additional data through to the function. It can be declared as any arbitrary type that you want, as long as it is the same type as the variable you passed to `nloptm` or `nloptc`
+
+### Nonlinear constraints in Fortran
+
+The `nloptc` function allows you to specify `m` nonlinear constraints via the subroutine `fc`, where `m` is any nonnegative integer. However, nonzero `m` is currently only supported by the `NLOPT_LD_MMA` and `NLOPT_LN_COBYLA` [algorithms](NLopt_Algorithms.md).
+
+In particular, the nonlinear constraints are of the form *fc*(*x*) ≤ 0, where the function fc is of the same form as the objective function described above:
+
+```
+subroutine fc(val, n, x, grad, need_gradient, fc_datum)
+```
+
+
+As above, upon return `val` should be the value of the constraint function at the point `x` (an array of length `n`), where the dimension `n` is identical to the one passed to `nloptc`. As for the objective function, if the argument `need_gradient` is not zero, then `grad` is an array of length `n` that should (upon return) be set to the gradient of the constraint function with respect to **x**. (For any algorithm listed as "derivative-free", the `need_gradient` argument will always be zero and the gradient need never be computed.)
+
+The `fc_datum` argument is based on the `fc_data` argument passed to `nloptc`, and may be used to pass any additional data through to the function, and is used to distinguish between different constraints.
+
+In particular, the constraint subroutine `fc` will be called (at most) `m` times for each `x`, and the *i*-th constraint (1 ≤ *i* ≤ *m*) will be passed an `fc_datum` argument equal to `fc_data` offset by the difference between `fc_data` and `fc_second_datum`. For example, suppose that your constraint function `fc` is parameterized by three numbers for each constraint, so you want your `fc_data` to be an array of length 3*m*: `double` `precision` `fc_data(3*m)`. Then, as the `fc_second_datum` argument to `nloptc`, you would pass `fc_data(4)`, which is the first data element for the second constraint. When `fc` is called the first time, it will be passed `fc_data(1:3)`; when it is called the second time it will be passed `fc_data(4:6)`, and so on in sequence.
+
+### Pseudorandom numbers in Fortran
+
+The Fortran equivalent of `nlopt_srand` (above), is:
+
+```
+call nlosr(seed)
+```
+
+
+where `seed` is an `integer`. The Fortran equivalent of `nlopt_srand_time` (above) is:
+
+```
+call nlosrt
+```
+
+
+### Version number in Fortran
+
+To determine the version number of NLopt at runtime, you can call:
+
+```
+call nloptv(major, minor, bugfix)
+```
+
+
+where the three arguments are `integer`s, as in `nlopt_version` above. For example, NLopt version 3.1.4 would return `major=3`, `minor=1`, and `bugfix=4`.
+
+### Mixed global/local search algorithm in Fortran
+
+The Fortran analogues of `nlopt_set_local_search_algorithm` and `nlopt_get_local_search_algorithm` are:
+
+```
+call nlosls(deriv, nonderiv, maxeval)
+call nlogls(deriv, nonderiv, maxeval)
+```
+
+
+where the arguments are all `integer`s and have the same meaning as those of `nlopt_set_local_search_algorithm` and `nlopt_get_local_search_algorithm`, above.
+
+### Population size for stochastic algorithms in Fortran
+
+The Fortran analogues of `nlopt_set_stochastic_population` and `nlopt_get_stochastic_population` are:
+
+```
+call nlossp(pop)
+call nlogsp(pop)
+```
+
+
+where the arguments are `integer`s and have the same meaning as the parameter of `nlopt_set_stochastic_population` and the return value of `nlopt_get_stochastic_population`, respectively.
+
+GNU Octave and Matlab interface
+-------------------------------
+
+We also provide an interface to NLopt that is callable from Matlab and [GNU Octave](https://en.wikipedia.org/wiki/GNU_Octave) (a free Matlab clone). This interface consists of two functions, `nlopt_minimize_constrained` and `nlopt_minimize`, which parallel the corresponding C functions above.
+
+### `nlopt_minimize_constrained` in Matlab
+
+```
+[xopt, fmin, retcode] = nlopt_minimize_constrained(algorithm, f, f_data, fc, fc_data, lb, ub, xinit, stop)
+```
+
+
+Minimize a nonlinear multivariable function `f(x,` `f_data{:})`, subject to optional nonlinear constraints described by `fc` and `fc_data` (see below), where `x` is a row vector of the optimization parameters, returning the optimal parameters found (`xopt`) along with the minimum function value (`fmin`) and a return code (`retcode`, positive on success and negative on failure). A variety of local and global optimization algorithms can be used, as specified by the `algorithm` parameter. `lb` and `ub` are row vectors giving the upper and lower bounds on `x`, `xinit` is a row vector giving the initial guess for `x`, and `stop` is a structure containing termination conditions (see below).
+
+Parameters:
+
+- `algorithm` — constant indicating the [optimization algorithm](NLopt_Algorithms.md) (predefined constants NLOPT_LN_NELDERMEAD etcetera are supplied as in C).
+- `f` — function handle (e.g. `@sin`) of the objective function being minimized, described below
+- `f_data` — cell array `{...}` of any additional arguments to pass to f (see below)
+- `fc` — cell array `{...}` of function handles to nonlinear inequality constraints (see below); can be empty `{}` for no nonlinear constraints
+- `fc_data` — cell array `{...}` of cell arrays: each element `fc_data{i}` is a cell array of additional arguments to pass to the function `fc{i}`; `length(fc_data)` must equal `length(fc)`
+- `lb` — row vector of lower bounds on each optimization parameter (set any component of `lb` to `-inf` for a parameter that is not bounded below)
+- `ub` — row vector of lower bounds on each optimization parameter (set any component of `ub` to `+inf` for a parameter that is not bounded above)
+- `xinit` — row vector containing a starting guess for the optimization parameters
+- `stop` — structure describing the termination conditions via a number of optional fields (see below)
+
+Notice that, unlike in C and Fortran, we do not explicitly pass the dimension *n* of the parameter space: *n* is implicitly the length of the `lb`, `ub`, and `xinit` vectors (which must all be the same length).
+
+#### Matlab objective function
+
+The parameter `f` should be a handle (`@`) to a function of the form:
+
+```
+ [val, gradient] = f(x, ...)
+```
+
+
+where `x` is a row vector, `val` is the function value *f*(**x**), and `gradient` is a row vector giving the gradient of the function with respect to `x`. The gradient is only used for gradient-based optimization algorithms; some of the algorithms are derivative-free and only require f to return val (its value), so for these algorithms you need not return the gradient. f can take additional arguments `(...)` which are passed via the argument `f_data`: `f_data` is a cell array of the additional arguments to pass to `f`. (Recall that cell arrays are specified by curly brackets { ... }. For example, pass `f_data={}` for functions that require no additional arguments.)
+
+#### Matlab nonlinear constraints
+
+Some of the algorithms (currently `NLOPT_LD_MMA` and `NLOPT_LN_COBYLA`) support nonlinear constraints. These (if any) are specified by `fc` and `fc_data`. `fc` is a cell array of function handles, and `fc_data` is a cell array of cell arrays of the corresponding arguments. Both must have the same length m, the number of nonlinear constraints. That is, `fc{i}` is a handle to a function of the form:
+
+```
+ [val, gradient] = fc(x, ...)
+```
+
+
+(where the `gradient` return value is only used for gradient-based algorithms), and the `...` arguments are given by `fc_data{i}{:}`.
+
+If you have no nonlinear constraints, i.e. `fc` = `fc_data` = `{}`, then it is equivalent to calling the the `nlopt_minimize` function below, which omits the `fc` and `fc_data` arguments.
+
+#### Matlab termination conditions
+
+`stop` describes the termination criteria, and is a structure with a number of optional fields:
+
+- `stop.fmin_max` — stop when *f* ≤ `fmin_max` is found
+- `stop.ftol_rel` — fractional tolerance on function value
+- `stop.ftol_abs` — absolute tolerance on function value
+- `stop.xtol_rel` — fractional tolerance on **x**
+- `stop.xtol_abs` — row vector of absolute tolerances on **x** components
+- `stop.maxeval` — maximum number of function evaluations
+- `stop.maxtime` — maximum run time in seconds
+- `stop.verbose` — > 0 indicates verbose output
+
+You do *not* need to set all of these fields; termination conditions corresponding to any fields that you do not set are ignored. As discussed in the [introduction](NLopt_Introduction#Termination_conditions.md), normally you only want one or two of these conditions. For example to set a relative **x** tolerance of 10<sup>−4</sup> and run for no more than 5 minutes, you would do:
+
+```
+stop.xtol_rel = 1e-4;
+stop.maxtime = 5 * 60;
+```
+
+
+and not create any other fields of `stop`.
+
+### `nlopt_minimize` in Matlab
+
+```
+[xopt, fmin, retcode] = nlopt_minimize(algorithm, f, f_data, lb, ub, xinit, stop)
+```
+
+
+This is equivalent to calling `nlopt_minimize_constrained` with no nonlinear constraints, i.e. `fc` = `fc_data` = `{}`.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt FAQ
+---
+
+General
+-------
+
+### What is NLopt?
+
+NLopt is a free/open-source library for nonlinear optimization.
+
+### Why use NLopt, when some of the same algorithms are available elsewhere?
+
+Several of the algorithms provided by NLopt are based on free/open-source packages by other authors, which we have put together under a common interface in NLopt. If you are using one of these packages and are happy with it, great!
+
+However, our experience is that, for nonlinear optimization, the best algorithm is highly problem-dependent; the best approach is to try several different techniques and see which one works best for *you*. NLopt makes this easy by providing a single package and a common interface for many different algorithms, callable from many different languages.
+
+Installation
+------------
+
+### Where can I install NLopt?
+
+NLopt should be straightforward to install on any Unix-like system (GNU/Linux is fine) with a C compiler (gcc is fine).
+
+It should be possible to compile under Windows, too, but to simplify life we plan to provide precompiled DLL files soon for Windows, cross-compiled using [MinGW](https://en.wikipedia.org/wiki/MinGW).
+
+Usage
+-----
+
+### I included your header file, but the compiler still complains
+
+You need to link to the NLopt library in addition to doing `#include` <nlopt.h>. On Unix, this means adding `-lnlopt` `-lm` at the *end* of your link command.
+
+### It's not converging
+
+The most common cause of convergence problems is if you use a gradient-based algorithm and return an incorrect gradient. It seems surprisingly easy to have bugs in code to compute derivatives—you should test it by comparing to finite-difference derivatives for a few random points and directions.
+
+You could also try switching algorithms to see if it is a problem in a particular algorithm (but check the gradient first!).
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt Fortran Reference
+---
+
+The NLopt includes an interface callable from the [Fortran programming language](https://en.wikipedia.org/wiki/Fortran).
+
+The main purpose of this section is to document the syntax and unique features of the Fortran API; for more detail on the underlying features, please refer to the C documentation in the [NLopt Reference](NLopt_Reference.md).
+
+Compiling and linking your Fortran program
+------------------------------------------
+
+To obtain the definitions of the NLopt constants in Fortran, your Fortran program/subroutine should include the following line:
+
+```
+include 'nlopt.f'
+```
+
+
+The `nlopt.f` file is installed into the `include` directory along with the C/C++ header files (by default, this is `/usr/local/include` ... you may need to include `-I/usr/local/include` in your Fortran compiler flags if this directory is not in your compiler's standard include path).
+
+When you compile your program you will have to link it to the NLopt library. On Unix, you would normally link with a command something like:
+
+*`compiler`*` `*`...source/object` `files...`*` -lnlopt -lm -o myprogram`
+
+where *compiler* is `f77`, `gfortran`, or whatever is appropriate for your machine.
+
+*Note:* the above example assumes that you have installed the NLopt library in a place where the compiler knows to find it (e.g. in a standard directory like `/usr/lib` or `/usr/local/lib`). If you installed somewhere else (e.g. in your home directory if you are not a system administrator), then you will need to use a `-L` flag to tell the compiler where to find the library. See [the installation manual](NLopt_Installation#Changing_the_installation_directory.md).
+
+Fortran vs. C API
+-----------------
+
+As explained in the [NLopt Tutorial](NLopt_Tutorial#Example_in_Fortran.md), there are a few simple rules that define the differences between the C and Fortran APIs:
+
+- All `nlopt_` functions are converted into `nlo_` subroutines, with return values converted into the first argument.
+- The `nlopt_opt` type corresponds to `integer*8`. (Technically, we could use any type that is big enough to hold a pointer on all platforms; `integer*8` is big enough for pointers on both 32-bit and 64-bit machines.)
+- Your objective/constraint subroutines must be declared as `external`, and must be defined as described below.
+- `include` `'nlopt.f'` in order to get the various constants like `NLOPT_LD_MMA`.
+- The C `int` or `unsigned` types become a Fortran `integer`, and the C `double` type becomes `real*8` or `double` `precision` in Fortran.
+
+The `nlopt_opt` object
+----------------------
+
+The NLopt API revolves around an "object" corresponding to the C type `nlopt_opt`. This object is internally a pointer, so it should be declared as an `integer*8` in Fortran (see above).
+
+Via functions that modify this object, all of the parameters of the optimization are specified (dimensions, algorithm, stopping criteria, constraints, objective function, etcetera), and then one finally calls `nlo_optimize` in order to perform the optimization. The object should normally be created via the constructor:
+
+```
+integer*8 opt
+opt = 0
+call nlo_create(opt, algorithm, n)
+```
+
+
+given an `integer` `algorithm` (see [NLopt Algorithms](NLopt_Algorithms.md) for possible values, defined in the `nlopt.f` include file) and the `integer` dimensionality of the problem (`n`, the number of optimization parameters). Just as in C, the algorithm is specified by constants of the form `NLOPT_MMA`, `NLOPT_COBYLA`, etcetera. If the constructor succeeds, `opt` will be nonzero after nlo_create, so you can check for an error by checking whether `opt` is zero (if you do this, be sure to initialize it to zero before calling nlo_create).
+
+When you are finished with the object, you must deallocate its associated storage by calling:
+
+```
+call nlo_destroy(opt)
+```
+
+
+There are also a copy subroutine `call` `nlo_copy(new_opt,` `opt)` to make a copy of a given object (equivalent to `nlopt_copy` in the C API).
+
+The algorithm and dimension parameters of the object are immutable (cannot be changed without constructing a new object), but you can query them for a given object by the subroutines:
+
+```
+call nlo_get_algorithm(algorithm, opt)
+call nlo_get_dimension(n, opt)
+```
+
+
+Objective function
+------------------
+
+The objective function is specified by calling one of the methods:
+
+```
+external f
+call nlo_set_min_objective(ires, opt, f, f_data)
+call nlo_set_max_objective(ires, opt, f, f_data)
+```
+
+
+depending on whether one wishes to minimize or maximize the objective function `f`, respectively. `ires` is an `integer` return value which is positive on success and negative on failure (see below for more specific [return-value meanings](#Return_values.md)).
+
+The function `f` should be of the form:
+
+```
+ subroutine f(result, n, x, grad, need_gradient, f_data)
+ integer need_gradient
+ double precision result, x(n), grad(n)
+ if (need_gradient.ne.0) then
+```
+
+` `*`..store` `gradient` `in` `grad...`*
+```
+ endif
+```
+
+` result = `*`...value` `of` `f(x)...`*
+```
+ end
+```
+
+
+The return value in `result` should be the value of the function at the point `x`, where `x` is an array of length `n` of the optimization parameters (the same as the dimension passed to the constructor).
+
+In addition, if the argument `need_gradient` is not zero, then `grad` is an array of length `n` which should (upon return) be set to the gradient of the function with respect to the optimization parameters at `x`. That is, `grad(i)` should upon return contain the partial derivative $\partial f / \partial x_i$, for $1 \leq i \leq n$. Not all of the optimization algorithms (below) use the gradient information: for algorithms listed as "derivative-free," the `grad` argument will always be empty and need never be computed. (For algorithms that do use gradient information, however, `grad` may still be empty for some calls.)
+
+The `f_data` argument can be used to pass through a single variable containing any data and any type to your subroutine. That is, whatever `f_data` variable you pass to `nlo_set_min_objective` is also passed to your function. NLopt does *not* pass a *copy* of your variable, it passes a reference to the original `f_data` variable. This means that you must call nlo_optimize while the `f_data` variable is still valid (e.g. it cannot be a local variable of a subroutine that has exited).
+
+Bound constraints
+-----------------
+
+The [bound constraints](NLopt_Reference#Bound_constraints.md) can be specified by calling the methods:
+
+```
+double precision lb(n), ub(n)
+call nlo_set_lower_bounds(ires, opt, lb)
+call nlo_set_upper_bounds(ires, opt, ub)
+```
+
+
+where `lb` and `ub` are arrays of length *n* (the same as the dimension passed to the `nlopt.opt` constructor), and `ires` is an `integer` [return value](#Return_values.md) (positive on success).
+
+For convenience, we also provide subroutines that take a single number as arguments, in order to set the lower/upper bounds for all optimization parameters to a single constant `value`.
+
+```
+call nlo_set_lower_bounds1(ires, opt, value)
+call nlo_set_upper_bounds1(ires, opt, value)
+```
+
+
+To retrieve the values of the lower/upper bounds, you can call one of:
+
+```
+call nlo_get_lower_bounds(ires, opt, lb)
+call nlo_get_upper_bounds(ires, opt, ub)
+```
+
+
+To specify an unbounded dimension, you can use ±`huge(lb(1))` in Fortran to specify ±∞, where `huge` is a Fortran 90 intrinsic function. If you have a Fortran 77 compiler that does not support this intrinsic, then you can call `nlo_get_upper_bounds` or `nlo_get_lower_bounds` first to get the default ±∞ upper/lower bounds.
+
+Nonlinear constraints
+---------------------
+
+Just as for [nonlinear constraints in C](NLopt_Reference#Nonlinear_constraints.md), you can specify nonlinear inequality and equality constraints by the methods:
+
+```
+call nlo_add_inequality_constraint(ires, opt, fc, fc_data, tol)
+call nlo_add_inequality_constraint(ires, opt, h, h_data, tol)
+```
+
+
+where the arguments `fc` and `h` have the same form as the objective function above. The `double` `precision` `tol` arguments specify a tolerance in judging feasibility for the purposes of stopping the optimization, as in C, and `ires` is an `integer` [return value](#Return_values.md) (positive on success).
+
+To remove all of the inequality and/or equality constraints from a given problem, you can call the following methods:
+
+```
+call nlo_remove_inequality_constraints(ires, opt)
+call nlo_remove_equality_constraints(ires, opt)
+```
+
+
+### Vector-valued constraints
+
+Just as for [nonlinear constraints in C](NLopt_Reference#Vector-valued_constraints.md), you can specify vector-valued nonlinear inequality and equality constraints by the subroutines
+
+```
+double precision tol(m)
+call nlo_add_inequality_mconstraint(ires, opt, m, c, c_data, tol)
+call nlo_add_equality_mconstraint(ires, opt, m, c, c_data, tol)
+```
+
+
+Here, *m* is the dimensionality of the constraint result and `tol` is a length-*m* array of the tolerances in each constraint dimension. The constraint subroutine `c` must be of the form:
+
+```
+ subroutine c(m, result, n, x, grad, need_gradient, f_data)
+ integer need_gradient
+ double precision result(m), x(n), grad(n,m)
+ if (need_gradient.ne.0) then
+```
+
+` `*`..store` `gradient` `in` `grad...`*
+```
+ endif
+```
+
+` `*`...store` `value` `of` `c(x)` `in` `result...`*
+```
+ end
+```
+
+
+This evaluates the constraint function(s) $\mathbf{c}(\mathbf{x})$ at the point `x`, an array of length `n` (the same as the dimension passed to `nlo_create`). Upon return, the output value of the constraints should be stored in `result`, an array of length `m` (the same as the dimension passed to `nlo_add_*_mconstraint`), so that `result(i)` stores *c*<sub>*i*</sub>.
+
+In addition, if `grad` is non-`NULL`, then `grad` is an *n*×*m* array that should, upon return, be set to the gradients of the constraint functions with respect to `x`. That is, $\part c_i / \part x_j$ is stored in `grad(j,i)`.
+
+An inequality constraint corresponds to $c_i \le 0$ for $1 \le i \le m$, and an equality constraint corresponds to $c_i = 0$, in both cases with tolerance `tol(i)` for purposes of termination criteria.
+
+(You can add multiple vector-valued constraints and/or scalar constraints in the same problem.)
+
+Stopping criteria
+-----------------
+
+As explained in the [C API Reference](NLopt_Reference#Stopping_criteria.md) and the [Introduction](NLopt_Introduction#Termination_conditions.md)), you have multiple options for different stopping criteria that you can specify. (Unspecified stopping criteria are disabled; i.e., they have innocuous defaults.)
+
+For each stopping criteria, there are (at least) two subroutines: a `set` subroutine to specify the stopping criterion, and a `get` subroutine to retrieve the current value for that criterion. The meanings of each criterion are exactly the same as in the C API. The first argument `ires` of each `set` subroutine is an `integer` [return value](#Return_values.md) (positive on success).
+
+```
+call nlo_set_stopval(ires, opt, stopval)
+call nlo_get_stopval(stopval, opt)
+```
+
+
+Stop when an objective value of at least `stopval` is found.
+
+```
+call nlo_set_ftol_rel(ires, opt, tol)
+call nlo_get_ftol_rel(tol, opt)
+```
+
+
+Set relative tolerance on function value.
+
+```
+call nlo_set_ftol_abs(ires, opt, tol)
+call nlo_get_ftol_abs(tol, opt)
+```
+
+
+Set absolute tolerance on function value.
+
+```
+call nlo_set_xtol_rel(ires, opt, tol)
+call nlo_get_xtol_rel(tol, opt)
+```
+
+
+Set relative tolerance on optimization parameters.
+
+```
+call nlo_set_xtol_abs(ires, opt, tol)
+call nlo_set_xtol_abs1(ires, opt, tol1)
+call nlo_get_xtol_abs(ires, opt, tol)
+```
+
+
+Set absolute tolerances on optimization parameters. The `tol` input must be an array of length `n` (the dimension specified in the `nlopt_opt` constructor). Alternatively, we provide the subroutine `nlo_set_xtol_abs1` where you pass a single number `tol1` in order to set the same tolerance for all optimization parameters. `nlo_get_xtol_abs` returns the tolerance array in `tol`.
+
+```
+call nlo_set_maxeval(ires, opt, maxeval)
+call nlo_get_maxeval(maxeval, opt)
+```
+
+
+Stop when the number of function evaluations exceeds the `integer` `maxeval`. (Zero or negative for no limit.)
+
+```
+call nlo_set_maxtime(ires, opt, maxtime)
+call nlo_get_maxtime(maxtime, opt)
+```
+
+
+Stop when the optimization time (in seconds) exceeds `maxtime` (`double` `precision`). (Zero or negative for no limit.)
+
+### Forced termination
+
+In certain cases, the caller may wish to *force* the optimization to halt, for some reason unknown to NLopt. For example, if the user presses Ctrl-C, or there is an error of some sort in the objective function. In this case, it is possible to tell NLopt to halt the optimization gracefully, returning the best point found so far, by calling the following subroutine from *within* your objective or constraint functions (exactly analogous to the corresponding [C routines](NLopt_Reference#Forced_termination.md)):
+
+```
+call nlo_force_stop(ires, opt)
+```
+
+
+`ires` is an `integer` [return value](#Return_values.md) (positive on success). More generally, you can set and retrieve a force-stop integer code `ival`, where a nonzero value indicates a forced stop.
+
+```
+call nlo_set_force_stop(ires, opt, ival)
+call nlo_get_force_stop(ires, opt, ival)
+```
+
+
+The force-stop value is reset to zero at the beginning of `nlopt_optimize`. Passing `ival=0` to `nlo_set_force_stop` tells NLopt *not* to force a halt.
+
+Performing the optimization
+---------------------------
+
+Once all of the desired optimization parameters have been specified in a given object `opt`, you can perform the optimization by calling:
+
+```
+double precision x(n), minf
+call nlo_optimize(ires, opt, x, minf)
+```
+
+
+On input, `x` is an array of length `n` (the dimension of the problem from the `nlopt.opt` constructor) giving an initial guess for the optimization parameters. Upon successful return, `x` contains the optimized values of the optimization parameters and `minf` contains the optimized objective-function value. `ires` is an `integer` [return value](#Return_values.md) (positive on success).
+
+### Return values
+
+The possible return values are the same as the [return values in the C API](NLopt_Reference#Return_values.md), with the corresponding integer constants defined in the `nlopt.f` include file.
+
+Local/subsidiary optimization algorithm
+---------------------------------------
+
+Some of the algorithms, especially MLSL and AUGLAG, use a different optimization algorithm as a subroutine, typically for local optimization. You can change the local search algorithm and its tolerances by calling:
+
+```
+nlo_set_local_optimizer(ires, opt, local_opt)
+```
+
+
+Here, `local_opt` is another `nlopt_opt` object (`integer*8`) whose parameters are used to determine the local search algorithm, its stopping criteria, and other algorithm parameters. (However, the objective function, bounds, and nonlinear-constraint parameters of `local_opt` are ignored.) The dimension `n` of `local_opt` must match that of `opt`. `ires` is an `integer` [return value](#Return_values.md) (positive on success).
+
+This function makes a copy of the `local_opt` object, so you can freely change or destroy your original `local_opt` afterwards without affecting `opt`.
+
+Initial step size
+-----------------
+
+Just as in the C API, you can [get and set the initial step sizes](NLopt_Reference#Initial_step_size.md) for derivative-free optimization algorithms. The Fortran equivalents of the C functions are the following methods:
+
+```
+double precision x(n) dx(n), dx1
+call nlo_set_initial_step(ires, opt, dx)
+call nlo_set_initial_step1(ires, opt, dx1)
+call nlo_get_initial_step(ires, opt, x, dx)
+```
+
+
+Here, `dx` is an array of the (nonzero) initial steps for each dimension. For convenience, you can also pass a single number `dx1` to `nlo_set_initial_step1` if you wish to use the same initial steps for all dimensions. `nlo_get_initial_step` sets `dx` to the initial step that will be used for a starting guess of `x` in `nlo_optimize(ires,` `opt,` `x,` `minf)`. `ires` is an `integer` [return value](#Return_values.md) (positive on success)
+
+Stochastic population
+---------------------
+
+Just as in the C API, you can [get and set the initial population](NLopt_Reference#Stochastic_population.md) for stochastic optimization algorithms, by the methods:
+
+```
+call nlo_set_population(ires, opt, ipop)
+call nlo_get_population(ipop, opt)
+```
+
+
+where `ipop` is an integer and `ires` is an `integer` [return value](#Return_values.md) (positive on success). (An `ipop` of zero implies that the heuristic default will be used.)
+
+Pseudorandom numbers
+--------------------
+
+For stochastic optimization algorithms, we use pseudorandom numbers generated by the [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_twister) algorithm, based on code from Makoto Matsumoto. By default, the [seed](https://en.wikipedia.org/wiki/Random_seed) for the random numbers is generated from the system time, so that you will get a different sequence of pseudorandom numbers each time you run your program. If you want to use a "deterministic" sequence of pseudorandom numbers, i.e. the same sequence from run to run, you can set the seed by calling:
+
+```
+call nlosr(iseed)
+```
+
+
+where `iseed` is an `integer`. To reset the seed based on the system time, you can call:
+
+```
+call nlosrt
+```
+
+
+(Normally, you don't need to call this as it is called automatically. However, it might be useful if you want to "re-randomize" the pseudorandom numbers after calling `nlosr` to set a deterministic seed.)
+
+Vector storage for limited-memory quasi-Newton algorithms
+---------------------------------------------------------
+
+Just as in the C API, you can get and set the [number *M* of stored vectors](NLopt_Reference#Vector_storage_for_limited-memory_quasi-Newton_algorithms.md) for limited-memory quasi-Newton algorithms:
+
+```
+call nlo_set_vector_storage(ires, opt, M)
+call nlo_get_vector_storage(M, opt)
+```
+
+
+(The default is *M*=0, in which case NLopt uses a heuristic nonzero value.)
+
+Version number
+--------------
+
+To determine the version number of NLopt at runtime, you can call:
+
+```
+call nloptv(major, minor, bugfix)
+```
+
+
+where the three arguments are `integer`s. For example, NLopt version 3.1.4 would return `major=3`, `minor=1`, and `bugfix=4`.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt Guile Reference
+---
+
+The NLopt includes an interface callable from the [Scheme programming language](https://en.wikipedia.org/wiki/Scheme_(programming_language)) as implemented in [GNU Guile](https://en.wikipedia.org/wiki/GNU_Guile) (which allows Scheme to be used as an extension language for other programs).
+
+The main purpose of this section is to document the syntax and unique features of the Guile API; for more detail on the underlying features, please refer to the C documentation in the [NLopt Reference](NLopt_Reference.md).
+
+Using the NLopt Guile API
+-------------------------
+
+To use NLopt in Python, your Python program should include the lines:
+
+```
+(use-modules (nlopt))
+```
+
+
+which imports the `nlopt` module.
+
+The `nlopt-opt` class
+---------------------
+
+The NLopt API revolves around an opaque "object", analogous to `nlopt::opt` in C++. Via "methods" of this object, all of the parameters of the optimization are specified (dimensions, algorithm, stopping criteria, constraints, objective function, etcetera), and then one finally calls the `opt.optimize` method in order to perform the optimization. The object should normally be created via the constructor:
+
+```
+(new-nlopt-opt algorithm n)
+```
+
+
+given an `algorithm` (see [NLopt Algorithms](NLopt_Algorithms.md) for possible values) and the dimensionality of the problem (`n`, the number of optimization parameters). Whereas the C algorithms are specified by `nlopt_algorithm` constants of the form `NLOPT_MMA`, `NLOPT_COBYLA`, etcetera, the Guile `algorithm` values are of the form `nlopt-MMA`, `nlopt-COBYLA`, etcetera (i.e., underscores are turned into dashes).
+
+There are also a copy constructor `(new-nlopt-opt` `opt)` to make a copy of a given object (equivalent to `nlopt_copy` in the C API).
+
+If there is an error in the constructor (or copy constructor, or assignment), an exception is thrown.
+
+The algorithm and dimension parameters of the object are immutable (cannot be changed without constructing a new object), but you can query them for a given object by the methods:
+
+```
+(nlopt-opt-get-algorithm opt)
+(nlopt-opt-get-dimension opt)
+```
+
+
+You can get a string description of the algorithm via:
+
+```
+(nlopt-opt-get-algorithm-name opt)
+```
+
+
+### Relationship to C++ interface
+
+In general, there is a simple relationship between the Guile interface and the [C++ interface](NLopt_C-plus-plus_Reference.md):
+
+- The `nlopt::` namespace becomes a prefix`nlopt-`, and `nlopt::opt` becomes `nlopt-opt-`. (Constants are prefixed with `NLOPT-`, however.)
+- Underscores (_) are turned into hyphens (-).
+- The `nlopt-opt` object becomes the first parameter of its methods.
+- `std::vector`<double> is turned into a Scheme `vector` (a `list` is also supported for input parameters).
+
+Objective function
+------------------
+
+The objective function is specified by calling one of the methods:
+
+```
+(nlopt-opt-set-min-objective opt f)
+(nlopt-opt-set-max-objective opt f)
+```
+
+
+depending on whether one wishes to minimize or maximize the objective function `f`, respectively. The function `f` should be of the form:
+
+```
+(define (f x grad)
+ (if grad
+ (begin `*`...set` `grad` `to` `gradient,` `in-place...`*`))
+ return `*`...value` `of` `f(x)...`*`)
+```
+
+
+The return value should be the value of the function at the point `x`, where `x` is a `vector` of length `n` of the optimization parameters (the same as the dimension passed to the constructor).
+
+In addition, if the argument `grad` is not `#f` (false), then `grad` is a `vector` of length `n` which should (upon return) be set to the gradient of the function with respect to the optimization parameters at `x`. That is, `(vector-ref` `grad` `i)` should upon return contain the partial derivative $\partial f / \partial x_i$, for $0 \leq i < n$, if `grad` is not `#f`. Not all of the optimization algorithms (below) use the gradient information: for algorithms listed as "derivative-free," the `grad` argument will always be empty and need never be computed. (For algorithms that do use gradient information, however, `grad` may still be empty for some calls.)
+
+Note that `grad` must be modified `in-place` by your function `f`, by using `(vector-set!` `grad` `i` *`value`*`)`.
+
+Bound constraints
+-----------------
+
+The [bound constraints](NLopt_Reference#Bound_constraints.md) can be specified by calling the methods:
+
+```
+(nlopt-opt-set-lower-bounds opt lb)
+(nlopt-opt-set-lower-bounds opt ub)
+```
+
+
+where `lb` and `ub` are vectors or lists of length *n* (the same as the dimension passed to the `nlopt.opt` constructor). For convenience, these are overloaded with functions that take a single number as arguments, in order to set the lower/upper bounds for all optimization parameters to a single constant.
+
+To retrieve the values of the lower/upper bounds, you can call one of:
+
+```
+(nlopt-opt-get-lower-bounds opt)
+(nlopt-opt-get-upper-bounds opt)
+```
+
+
+both of which return vectors.
+
+To specify an unbounded dimension, you can use `(inf)` or `(-` `(inf))` in Guile to specify ±∞, respectively.
+
+Nonlinear constraints
+---------------------
+
+Just as for [nonlinear constraints in C](NLopt_Reference#Nonlinear_constraints.md), you can specify nonlinear inequality and equality constraints by the methods:
+
+```
+(nlopt-opt-add-inequality-constraint opt fc tol)
+(nlopt-opt-add-equality-constraint opt h tol)
+```
+
+
+where the arguments `fc` and `h` have the same form as the objective function above. The (optional) `tol` arguments specify a tolerance in judging feasibility for the purposes of stopping the optimization, as in C (defaulting to zero if they are omitted).
+
+To remove all of the inequality and/or equality constraints from a given problem, you can call the following methods:
+
+```
+(nlopt-opt-remove-inequality-constraints opt)
+(nlopt-opt-remove-equality-constraints opt)
+```
+
+
+Stopping criteria
+-----------------
+
+As explained in the [C API Reference](NLopt_Reference#Stopping_criteria.md) and the [Introduction](NLopt_Introduction#Termination_conditions.md)), you have multiple options for different stopping criteria that you can specify. (Unspecified stopping criteria are disabled; i.e., they have innocuous defaults.)
+
+For each stopping criteria, there are (at least) two method: a `set` method to specify the stopping criterion, and a `get` method to retrieve the current value for that criterion. The meanings of each criterion are exactly the same as in the C API.
+
+```
+(nlopt-opt-set-stopval opt stopval)
+(nlopt-opt-get-stopval opt)
+```
+
+
+Stop when an objective value of at least `stopval` is found.
+
+```
+(nlopt-opt-set-ftol-rel opt tol)
+(nlopt-opt-get-ftol-rel opt tol)
+```
+
+
+Set relative tolerance on function value.
+
+```
+(nlopt-opt-set-ftol-abs opt tol)
+(nlopt-opt-get-ftol-abs opt tol)
+```
+
+
+Set absolute tolerance on function value.
+
+```
+(nlopt-opt-set-xtol-rel opt tol)
+(nlopt-opt-get-xtol-rel opt tol)
+```
+
+
+Set relative tolerance on optimization parameters.
+
+```
+(nlopt-opt-set-xtol-abs opt tol)
+(nlopt-opt-get-xtol-abs opt tol)
+```
+
+
+Set absolute tolerances on optimization parameters. The `tol` input must be a vector or list of length `n` (the dimension specified in the `nlopt.opt` constructor); alternatively, you can pass a single number in order to set the same tolerance for all optimization parameters. `get-xtol-abs()` returns the tolerances as a vector.
+
+```
+(nlopt-opt-set-maxeval opt maxeval)
+(nlopt-opt-get-maxeval opt)
+```
+
+
+Stop when the number of function evaluations exceeds `maxeval`. (0 or negative for no limit.)
+
+```
+(nlopt-opt-set-maxtime opt maxtime)
+(nlopt-opt-get-maxtime opt)
+```
+
+
+Stop when the optimization time (in seconds) exceeds `maxtime`. (0 or negative for no limit.)
+
+Performing the optimization
+---------------------------
+
+Once all of the desired optimization parameters have been specified in a given object `opt`, you can perform the optimization by calling:
+
+```
+(nlopt-opt-optimize opt x)
+```
+
+
+On input, `x` is a vector or list of length `n` (the dimension of the problem from the `nlopt.opt` constructor) giving an initial guess for the optimization parameters. The return value is a vector containing the optimized values of the optimization parameters.
+
+You can call the following methods to retrieve the optimized objective function value from the last `optimize` call, and also the return code (including negative/failure return values) from the last `optimize` call:
+
+```
+(nlopt-opt-last-optimum-value opt)
+(nlopt-opt-last-optimize-result opt)
+```
+
+
+The return code (see below) is positive on success, indicating the reason for termination. On failure (negative return codes), `optimize` throws an exception (see [Exceptions](#Exceptions.md), below).
+
+### Return values
+
+The possible return values are the same as the [return values in the C API](NLopt_Reference#Return_values.md), except that the `NLOPT_` prefix is replaced with the `NLOPT-` namespace. That is, `NLOPT_SUCCESS` becomes `NLOPT-SUCCESS`, etcetera.
+
+Exceptions
+----------
+
+The [Error codes (negative return values)](NLopt_Reference#Error_codes_(negative_return_values).md) in the C API are replaced in the Guile API by thrown exceptions. The exception key takes the form of a Scheme symbol. The following exception keys are thrown by the various routines:
+
+```
+runtime-error
+```
+
+Generic failure, equivalent to `NLOPT_FAILURE`.
+
+```
+invalid-argument
+```
+
+Invalid arguments (e.g. lower bounds are bigger than upper bounds, an unknown algorithm was specified, etcetera), equivalent to `NLOPT_INVALID_ARGS`.
+
+```
+bad-alloc
+```
+
+Ran out of memory (a memory allocation failed), equivalent to `NLOPT_OUT_OF_MEMORY`.
+
+`roundoff-limited` (subclass of `Exception`)
+Halted because roundoff errors limited progress, equivalent to `NLOPT_ROUNDOFF_LIMITED`.
+
+`forced-stop` (subclass of `Exception`)
+Halted because of a [forced termination](#Forced_termination.md): the user called `opt.force_stop()` from the user’s objective function. Equivalent to `NLOPT_FORCED_STOP`.
+
+Currently, NLopt does not catch any exceptions that you might throw from your objective or constraint functions. (In the future, we might catch these exceptions, halt the optimization gracefully, and then re-throw, as in Python or C++, but this is not yet implemented.) So, throwing an exception in your objective/constraint may result in a memory leak.
+
+To catch an [exception in Guile](http://www.gnu.org/software/guile/manual/html_node/Exceptions.html), you need to define a [throw-handler](http://www.gnu.org/software/guile/manual/html_node/Throw-Handlers.html) function. For example, the following code calls `nlopt-opt-optimize`, catches *any* exception (a key of `#t` in `catch`), and prints out the error return code:
+
+```
+(define xopt
+ (catch #t
+ (lambda () (nlopt-opt-optimize opt x))
+ (lambda (key . args)
+ (display "Caught exception ") (display key) (display " ") (display args) (newline)
+ (display "NLopt result ") (display (nlopt-opt-last-optimize-result opt)) (newline)
+ #f)
+ ))
+```
+
+
+Note that the [catch statement](http://www.gnu.org/software/guile/manual/html_node/Catch.html) takes three arguments: the first is a key to catch (\#t for all), the second is a [thunk](https://en.wikipedia.org/wiki/Thunk) function to do whatever it is that might throw exceptions (the equivalent of a C++ `try` block), and the third is a function that is called if there is an exception (the equivalent of a C++ `catch` block). Note that `xopt` is set to the return value of `nlopt-opt-optimize` on success, or `#f` (the return value of our throw handler) on an exception.
+
+Local/subsidiary optimization algorithm
+---------------------------------------
+
+Some of the algorithms, especially MLSL and AUGLAG, use a different optimization algorithm as a subroutine, typically for local optimization. You can change the local search algorithm and its tolerances by calling:
+
+```
+(nlopt-opt-set-local-optimizer opt local-opt)
+```
+
+
+Here, `local-opt` is another `nlopt-opt` object whose parameters are used to determine the local search algorithm, its stopping criteria, and other algorithm parameters. (However, the objective function, bounds, and nonlinear-constraint parameters of `local-opt` are ignored.) The dimension `n` of `local-opt` must match that of `opt`.
+
+This function makes a copy of the `local-opt` object, so you can freely change your original `local-opt` afterwards without affecting `opt`.
+
+Initial step size
+-----------------
+
+Just as in the C API, you can [get and set the initial step sizes](NLopt_Reference#Initial_step_size.md) for derivative-free optimization algorithms. The Guile equivalents of the C functions are the following methods:
+
+```
+(nlopt-opt-set-initial-step opt dx)
+(nlopt-opt-get-initial-step opt x)
+```
+
+
+Here, `dx` is a vector or list of the (nonzero) initial steps for each dimension, or a single number if you wish to use the same initial steps for all dimensions. `nlopt-opt-get-initial-step` returns the initial step (vector) that will be used for a starting guess of `x` in `(nlopt-opt-optimize` `opt` `x)`.
+
+Stochastic population
+---------------------
+
+Just as in the C API, you can [get and set the initial population](NLopt_Reference#Stochastic_population.md) for stochastic optimization algorithms, by the methods:
+
+```
+(nlopt-opt-set-population opt pop)
+(nlopt-opt-get-population opt)
+```
+
+
+(A `pop` of zero implies that the heuristic default will be used.)
+
+Pseudorandom numbers
+--------------------
+
+For stochastic optimization algorithms, we use pseudorandom numbers generated by the [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_twister) algorithm, based on code from Makoto Matsumoto. By default, the [seed](https://en.wikipedia.org/wiki/Random_seed) for the random numbers is generated from the system time, so that you will get a different sequence of pseudorandom numbers each time you run your program. If you want to use a "deterministic" sequence of pseudorandom numbers, i.e. the same sequence from run to run, you can set the seed by calling:
+
+```
+(nlopt-srand seed)
+```
+
+
+where `seed` is an integer. o reset the seed based on the system time, you can call:
+
+```
+(nlopt-srand-time)
+```
+
+
+(Normally, you don't need to call this as it is called automatically. However, it might be useful if you want to "re-randomize" the pseudorandom numbers after calling `nlopt-srand` to set a deterministic seed.)
+
+Vector storage for limited-memory quasi-Newton algorithms
+---------------------------------------------------------
+
+Just as in the C API, you can get and set the [number *M* of stored vectors](NLopt_Reference#Vector_storage_for_limited-memory_quasi-Newton_algorithms.md) for limited-memory quasi-Newton algorithms, via the functions:
+
+```
+(nlopt-opt-set-vector-storage opt M)
+(nlopt-opt-get-vector-storage opt)
+```
+
+
+(The default is *M*=0, in which case NLopt uses a heuristic nonzero value.)
+
+Version number
+--------------
+
+To determine the version number of NLopt at runtime, you can call:
+
+```
+(nlopt-version-major)
+(nlopt-version-minor)
+(nlopt-version-bugfix)
+```
+
+
+For example, NLopt version 3.1.4 would return `major=3`, `minor=1`, and `bugfix=4`.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt Installation
+---
+
+The installation of NLopt is fairly standard and straightforward, at least on Unix-like systems (GNU/Linux is fine). It doesn't require any particular packages to be installed except for a C compiler, although you need to have [Octave](https://en.wikipedia.org/wiki/GNU_Octave) and/or Matlab installed if you want to install the Octave and/or Matlab plugins, respectively.
+
+In particular, NLopt uses the standard [Autoconf](https://en.wikipedia.org/wiki/GNU_Autoconf) `configure` script, which means that you compile it via:
+
+```
+./configure
+make
+```
+
+
+in the `nlopt` directory. Then, you would switch to be the `root` user, or use the `sudo` command, to install the NLopt libraries and header files via:
+
+```
+make install
+```
+
+
+By default, this installs the NLopt static library (`libnlopt.a`) in `/usr/local/lib` and the NLopt header file (`nlopt.h`) in `/usr/local/include`, as well manual pages and a few other files.
+
+In the following, we describe a few details of this installation process, including how to change the installation location.
+
+Changing the installation directory
+-----------------------------------
+
+You may wish to install NLopt in a directory other than `/usr/local`, especially if you do not have administrator access to your machine. You can do this using the `--prefix` argument to the `configure` script.
+
+For example, suppose that you want to install into the `install` subdirectory of your home directory (`$HOME`). You would do:
+
+```
+./configure --prefix=$HOME/install
+make
+make install
+```
+
+
+This will create the directories `$HOME/install/lib` etcetera and install NLopt into them. However, now when you compile code using NLopt, you will need to tell the compiler where to find the NLopt header files (using `-I`) and libraries (using `-L`) with something like:
+
+```
+cc -I$HOME/install/include myprogram.c -L$HOME/install/lib -lnlopt -lm -o myprogram
+```
+
+
+See also below for how to change the installation directories for Octave, Matlab, and Guile plugins, if you are installing those.
+
+Note also that the `--prefix` flag will change the location where the Python plugins are installed, so you may need to change the [Python module search path](http://docs.python.org/tutorial/modules.html#the-module-search-path) via the `PYTHONPATH` environment variable.
+
+Shared libraries
+----------------
+
+By default, NLopt compiles as a static library. This means that each program you link to NLopt will make a separate copy of the library, which wastes a little disk space. The alternative is to compile NLopt as a shared library (also called a dynamic-link library). While more efficient in terms of disk space etcetera, shared libraries require a bit more care to install properly, which is why we don't install them by default.
+
+Compiling NLopt as a shared library is easy. Just add `--enable-shared` to the `configure` flags, as in:
+
+```
+./configure --enable-shared
+```
+
+
+Then you run `make` and `make` `install` as usual.
+
+However, at this point you need to tell the operating system where to find the shared library, so that the runtime linker works properly. There are at least two ways to do this. First, you can use the `LD_LIBRARY_PATH` environment variable. For example, if you installed into the `/foo/bar` directory, so that the library is in `/foo/bar/lib`, then you would do
+
+```
+export LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:/foo/bar/lib
+```
+
+
+in the [bash](https://en.wikipedia.org/wiki/Bash) shell, or
+
+```
+setenv LD_LIBRARY_PATH ${LD_LIBRARY_PATH}:/foo/bar/lib
+```
+
+
+in [csh](https://en.wikipedia.org/wiki/csh) or [w:tcsh](https://en.wikipedia.org/wiki/tcsh).
+
+Alternatively, in GNU/Linux systems, you can add the library directory to the system-wide file `/etc/ld.so.conf` and then (as root) run `/sbin/ldconfig`. [Category:NLopt](index.md)
+
+Octave and Matlab plugins
+-------------------------
+
+When you compile NLopt using the above commands, it will automatically compile plugins for both Matlab and GNU Octave (a free Matlab clone) if the latter programs are installed. On most current systems, Matlab and Octave plugins require NLopt to be compiled as a shared library (see above).
+
+### Matlab
+
+In particular, for Matlab plugins to be installed, you should to have the Matlab `mex` compiler command in your [Unix PATH](http://kb.iu.edu/data/acar.html). Alternatively, you can specify the explicit path to the `mex` by passing a `MEX` variable to `configure`, via:
+
+`./configure MEX=`*`/path/to/mex`*
+
+Some versions of Matlab also require that you compile NLopt as a shared library in order to produce a Matlab plugin; see below.
+
+By default, the Matlab plugins (along with help files and other `.m` files) are installed into the `MATLABPATH` printed out by `matlab` `-n` (which gives some directory within your Matlab installation directory), so that they will be available to all Matlab users. (This requires `matlab` to be in your `PATH` too; alternatively, you can pass `MATLAB=/path/to/matlab` to `configure`.) You can override this default (e.g. if you don't have administrator access on your machine) by passing a `MEX_INSTALL_DIR` to `configure`, via (in addition to other `configure` arguments):
+
+`./configure MEX_INSTALL_DIR=`*`dir`*
+
+to install the Matlab plugins in directory *dir*. In this case, however, when you run Matlab you will either need to run in the *dir* directory or explicitly add *dir* to your Matlab path (see the Matlab `path` command).
+
+### Octave
+
+For the Octave plugins to be installed, you need to have the Octave `mkoctfile` program in your PATH. `mkoctfile` is Octave's equivalent of `mex`. If you are using a GNU/Linux system, and you installed Octave using one of the precompiled packages for your distribution, then you probably need to install a *separate package* to get `mkoctfile`. For example, on Debian you need to install the `octave-headers` package, and on Redhat you need the `octave-devel` package.
+
+By default, the compiled Octave plugins (`.oct` files) are installed into the systemwide `site/oct` directory (usually something like `/usr/lib/octave/2.1.73/site/oct/i486-pc-linux-gnu`), and the .m script files are installed into the systemwide `site/m` directory (usually something like `/usr/share/octave/2.1.73/site/m/`). You can change these defaults by passing `OCT_INSTALL_DIR` and `M_INSTALL_DIR`, respectively, to the configure script, via:
+
+`./configure OCT_INSTALL_DIR=`*`octdir`*` M_INSTALL_DIR=`*`mdir`*
+
+(If you only pass `OCT_INSTALL_DIR`, the default `M_INSTALL_DIR=$OCT_INSTALL_DIR`.) In this case, however you will either need to run Octave in the directory where these files are installed or explicitly add those directories to the Octave path (see the Octave `path` command).
+
+Python plugins
+--------------
+
+If [Python](https://en.wikipedia.org/wiki/Python_(programming_language)) is installed on your machine, and you configured NLopt as a shared library (see above), then NLopt will automatically compile and install a Python `nlopt` module. You also need [NumPy](https://en.wikipedia.org/wiki/NumPy) to be installed, as NLopt's Python interface uses NumPy array types.
+
+To specify a particular version or location of Python, use the `PYTHON` variable to set the name of the `python` executable:
+
+`./configure PYTHON=`*`python`*
+
+GNU Guile plugins
+-----------------
+
+If [Guile](https://en.wikipedia.org/wiki/GNU_Guile) is installed on your machine, and you configured NLopt as a shared library (see above), then a Guile `nlopt` module will automatically be compiled and installed.
+
+Note that many GNU/Linux distributions come with only the Guile program and shared libraries pre-installed; to compile the NLopt plugin you will also need the Guile programming header files, which are usually in a `guile-dev` or `guile-devel` package that you must install separately.
+
+If you want to specify a particular version or a nonstandard location of Guile, you should use the `GUILE_CONFIG` and `GUILE` variables to specify the locations of the `guile-config` and `guile` programs:
+
+`./configure GUILE=`*`guile`*` GUILE_CONFIG=`*`guile-config`*
+
+(The `configure` script uses these programs to determine the compiler flags and installation directories for Guile plugins.)
+
+By default, the Guile plugin is installed into the system-wide site directory (the value of the `(%site-dir)` function in Guile), typically something like `/usr/share/guile/site`. If you want to install somewhere else (e.g. if you do not have administrator access), you can specify a different directory by setting `GUILE_INSTALL_DIR` on the `configure` command line:
+
+`./configure GUILE_INSTALL_DIR=`*`dir`*
+
+Note, however, that if you do this then Guile may not know where to load the `nlopt` module from. You can [update the Guile load path](http://www.gnu.org/software/guile/manual/html_node/Build-Config.html) by changing the `%load-path` variable in Guile or using the `GUILE_LOAD_PATH` environment variable.
+
+NLopt with C++ algorithms
+-------------------------
+
+NLopt, as-is, is callable from C, C++, and Fortran, with optional Matlab and GNU Octave plugins (and even installs an `nlopt.hpp` C++ header file to allow you to call it in a more C++ style). By default, it includes only subroutines written in C (or written in Fortran and converted to C), to simplify linking. If you configure with:
+
+```
+./configure --with-cxx
+```
+
+
+however, it will also include algorithms implemented in C++ (currently, just the StoGO algorithm), and the resulting library will be called `libnlopt_cxx` and is linked with `-lnlopt_cxx`.
+
+The `libnlopt_cxx` has the *same* interface as the ordinary NLopt library, and can *still* be called from ordinary C and Fortran programs. However, to use it you must also *link* with the C++ standard libraries. The easiest way to do this is to link with the C++ linker: compile your source files into `.o` object files, and then call the C++ compiler to link these `.o` files with `-lnlopt_cxx` into your executable program.
+
+It is because this linking process is somewhat annoying, and it only adds a single more algorithm (StoGO) to NLopt, that by default we omit StoGO to create a library that does not require the C++ standard libraries to link.
--- /dev/null
+---
+# NLopt Introduction
+---
+
+In this chapter of the manual, we begin by giving a general overview of the optimization problems that NLopt solves, the key distinctions between different types of optimization algorithms, and comment on ways to cast various problems in the form NLopt requires. We also describe the background and goals of NLopt.
+
+Optimization problems
+---------------------
+
+NLopt addresses general nonlinear optimization problems of the form:
+
+$$\min_{\mathbf{x}\in\mathbb{R}^n} f(\mathbf{x})$$,
+
+where *f* is the **objective function** and **x** represents the *n* **optimization parameters** (also called *design variables* or *decision parameters*). This problem may optionally be subject to the **bound constraints** (also called *box constraints*):
+
+$$lb_i \leq x_i \leq ub_i$$ for $i=1,\ldots,n$
+
+given lower bounds *lb* and upper bounds *ub* (which may be −∞ and/or +∞, respectively, for partially or totally unconstrained problems). (If $lb_i = ub_i$, that parameter is effectively eliminated.) One may also optionally have *m* **nonlinear inequality constraints** (sometimes called a **nonlinear programming** problem):
+
+$$fc_i(\mathbf{x}) \leq 0$$ for $i=1,\ldots,m$
+
+for **constraint functions** *fc*<sub>*i*</sub>(**x**). Some of the NLopt algorithms also support *p* **nonlinear equality constraints**:
+
+$$h_i(\mathbf{x}) = 0$$ for $i=1,\ldots,p$
+
+(More generally, several constraints at once might be combined into a single function that returns a vector-valued result.)
+
+A point **x** that satisfies all of the bound, inequality, and equality constraints is called a **feasible point**, and the set of all feasible points is the **feasible region**.
+
+*Note:* in this introduction, we follow the usual mathematical convention of letting our indices begin with one. In the C programming language, however, NLopt follows C's zero-based conventions (e.g. *i* goes from 0 to *m*−1 for the constraints).
+
+### Global versus local optimization
+
+NLopt includes algorithms to attempt either *global* or *local* optimization of the objective.
+
+**Global optimization** is the problem of finding the feasible point **x** that minimizes the objective *f*(**x**) over the *entire* feasible region. In general, this can be a *very difficult* problem, becoming exponentially harder as the number *n* of parameters increases. In fact, unless special information about *f* is known, it is not even possible to be certain whether one has found the true global optimum, because there might be a sudden dip of *f* hidden somewhere in the parameter space you haven't looked at yet. However, NLopt includes several global optimization algorithms that work well on reasonably well-behaved problems, if the dimension *n* is not too large.
+
+**Local optimization** is the *much easier* problem of finding a feasible point **x** that is only a *local* minimum: *f*(**x**) is less than or equal to the value of *f* for all nearby feasible points (the intersection of the feasible region with at least some small neighborhood of **x**). In general, a nonlinear optimization problem may have *many* local minima, and which one is located by an algorithm typically depends upon the starting point that the user supplies to the algorithm. Local optimization algorithms, on the other hand, can often quickly locate a local minimum even in very high-dimensional problems (especially using gradient-based algorithms). (An algorithm that is guaranteed to find some *local* minimum from any feasible starting point is, somewhat confusingly, called *globally convergent*.)
+
+In the special class of **convex optimization** problems, for which both the objective and inequality constraint functions are [convex](https://en.wikipedia.org/wiki/Convex_function) (and the equality constraints are [affine](https://en.wikipedia.org/wiki/Affine_transformation) or in any case have [convex](https://en.wikipedia.org/wiki/Convex_set) [level sets](https://en.wikipedia.org/wiki/Level_set)), there is only *one* local minimum value of *f* , so that a *local* optimization method finds a *global* optimum. $$There may, however, be more than one point **x** that yield the same minimum *f*(**x**), with the optimum points forming a convex subset of the (convex) feasible region.$$ Typically, convex problems arise from functions of special analytical forms, such as linear programming problems, semidefinite programming, quadratic programming, and so on, and specialized techniques are available to solve these problems very efficiently. NLopt includes only general methods that do not assume convexity; if you have a provably convex problem, you may be better off with a different software package, such as the [CVX package](http://www.stanford.edu/~boyd/cvx/) from Stanford.
+
+### Gradient-based versus derivative-free algorithms
+
+Especially for local optimization, the most efficient algorithms typically require the user to supply the gradient ∇*f* in addition to the value *f*(**x**) for any given point **x** (and similarly for any nonlinear constraints). This exploits the fact that, in *principle*, the gradient can almost always be computed at the same time as the value of *f* using very little additional computational effort (at worst, about the same as that of evaluating *f* a second time). If a quick way to compute the derivative of *f* is not obvious, one typically finds ∇*f* using an [adjoint method](http://math.mit.edu/~stevenj/18.336/adjoint.pdf), or possibly using [automatic differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation) tools. Gradient-based methods are critical for the efficient optimization of very high-dimensional parameter spaces (e.g. *n* in the thousands or more).
+
+On the other hand, computing the gradient is sometimes cumbersome and inconvenient if the objective function is supplied as a complicated program. It may even be impossible, if *f* is not differentiable (or worse, is discontinuous). In such cases, it is often easier to use a *derivative-free* algorithm for optimization, which only requires that the user supply the function *values* *f*(**x**) for any given point **x**. Such methods typically must evaluate *f* for at *least* several-times-*n* points, however, so they are best used when *n* is small to moderate (up to hundreds).
+
+NLopt provides both derivative-free and gradient-based algorithms with a common interface.
+
+**Note**: If you find yourself computing the gradient by a finite-difference approximation (e.g. $\partial f/\partial x \approx [f(x+\Delta x) - f(x -\Delta x)]/2\Delta x$ in one dimension), then you should probably use a derivative-free algorithm instead. Finite-difference approximations are not only expensive (2*n* function evaluations for the gradient using center differences), but they are also notoriously susceptible to roundoff errors unless you are very careful. On the other hand, finite-difference approximations are very useful to *check* that your *analytical* gradient computation is correct—this is always a good idea, because in my experience it is very easy to have bugs in your gradient code, and an incorrect gradient will cause weird problems with a gradient-based optimization algorithm.
+
+### Equivalent formulations of optimization problems
+
+There are many equivalent ways to formulate a given optimization problem, even within the framework defined above, and finding the best formulation can be something of an art.
+
+To begin with a trivial example, suppose that you want to *maximize* the function *g*(**x**). This is equivalent to minimizing the function *f*(**x**)=−*g*(**x**). Because of this, there is no need for NLopt to provide separate maximization routines in addition to its minimization routines—the user can just flip the sign to do maximization. As a convenience, however, NLopt provides a maximization interface (which performs the necessary sign flips for you, internally).
+
+A more interesting example is that of a **minimax** optimization problem, where the objective function *f*(**x**) is the maximum of *N* functions:
+
+$$f(\mathbf{x}) = \max \{ g_1(\mathbf{x}), g_2(\mathbf{x}), \ldots, g_N(\mathbf{x}) \}$$
+
+You could, of course, pass this objective function directly to NLopt, but there is a problem: it is not everywhere differentiable (it is only piecewise differentiable, assuming *g<sub>k</sub>* is differentiable). Not only does this mean that the most efficient gradient-based algorithms are inapplicable, but even the derivative-free algorithms may be slowed down considerably. Instead, it is possible to formulate the *same* problem as a differentiable problem by adding a *dummy* variable *t* and *N* new nonlinear constraints (in addition to any other constraints):
+
+$$\min_{x\in\mathbb{R}^n, t\in\mathbb{R}} t$$
+
+
+subject to $g_k(\mathbf{x}) - t \leq 0$ for $k=1,2,\ldots,N$.
+
+This solves *exactly* the same minimax problem, but now we have a differentiable objective and constraints, assuming that the functions *g*<sub>*k*</sub> are individually differentiable. Notice that, in this case, the objective function by itself is the boring linear function *t*, and all of the interesting stuff is in the constraints. This is typical of many nonlinear programming problems.
+
+Yet another example would be minimizing the absolute value $|g(\mathbf{x})|$ of some function *g*(**x**). This is equivalent to minimizing $\max \{ g(\mathbf{x}), -g(\mathbf{x}) \}$, however, and can therefore be transformed into differentiable nonlinear constraints as in the minimax example above.
+
+### Equality constraints
+
+Suppose that you have one or more **nonlinear equality constraints**
+
+$$h_i(\mathbf{x}) = 0$$.
+
+In *principle*, each equality constraint can be expressed by two inequality constraints $h_i(\mathbf{x}) \leq 0$ and $-h_i(\mathbf{x}) \leq 0$, so you might think that any code that can handle inequality constraints can automatically handle equality constraints. In practice, this is not true—if you try to express an equality constraint as a pair of nonlinear inequality constraints, some algorithms will fail to converge.
+
+Equality constraints sometimes require special handling because they reduce the *dimensionality* of the feasible region, and not just its size as for an inequality constraint. Only some of the NLopt algorithms (AUGLAG, COBYLA, and ISRES) currently support nonlinear equality constraints.
+
+#### Elimination
+
+Sometimes, it is possible to handle equality constraints by an **elimination** procedure: you use the equality constraint to explicitly solve for some parameters in terms of other unknown parameters, and then only pass the latter as optimization parameters to NLopt.
+
+For example, suppose that you have a *linear* (technically, affine) equality constraint:
+
+$$A\mathbf{x} = \mathbf{b}$$
+
+for some constant matrix *A*. Given a particular solution **ξ** of these equations and a matrix *N* whose columns are a basis for the nullspace of *A*, one can express all possible solutions of these linear equations in the form:
+
+$$\mathbf{x} = \boldsymbol{\xi} + N\mathbf{z}$$
+
+for unknown vectors **z**. You could then pass **z** as the optimization parameters to NLopt, rather than **x**, and thus eliminate the equality constraint.
+
+(Some care is required in [numerically computing the nullspace](https://en.wikipedia.org/wiki/Kernel_(matrix)#Numerical_computation_of_null_space) matrix *N*, because [rounding errors](https://en.wikipedia.org/wiki/Round-off_error) will tend to make the matrix *A* less singular than it should be. A standard technique is to compute the [SVD](https://en.wikipedia.org/wiki/Singular_value_decomposition) of *A* and set any singular values less than some threshold to zero.)
+
+#### Penalty functions
+
+Another popular approach to equality constraints (and inequality constraints, for that matter) is to include some sort of **penalty function** in the objective function, which penalizes **x** values that violate the constraints. A standard technique of this sort is known as the **augmented Lagrangian** approach, and a variant of this approach is implemented in NLopt's [AUGLAG algorithm](NLopt_Algorithms#Augmented_Lagrangian_algorithm.md).
+
+(For inequality constraints, a variant of the penalty idea is a **barrier method**: this is simply a penalty that diverges as you approach the constraint, which forces the optimization to stay within the feasible region.)
+
+Termination conditions
+----------------------
+
+For any optimization algorithm, one must supply some **termination conditions** specifying when the algorithm halts. Ideally, the algorithm should halt when the optimum is found to within some desired tolerance. In practice, however, because the true optimum is not known *a priori*, one uses some heuristic estimate for the error in the solution instead of the actual error.
+
+NLopt gives the user a choice of several different termination conditions. You do *not* need to specify *all* of these termination conditions for any given problem. You should just set the conditions you want; NLopt will terminate when the *first* one of the specified termination conditions is met (i.e. the *weakest* condition you specify is what matters).
+
+The termination conditions supported by NLopt are:
+
+### Function value and parameter tolerances
+
+First, you can specify a fractional tolerance ftol_rel and an absolute tolerance ftol_abs on the function values. Ideally, these would be the maximum fractional and absolute error compared to the exact minimum function value, but this is impossible because the minimum is not known. Instead most algorithms implement these as a tolerance for the decrease Δf in the function value from one iteration to next (or something similar to that): the algorithm stops if |Δf|/|f| is less than ftol_rel, or |Δf| is less than ftol_abs.
+
+Similarly, you can specify a fractional tolerance xtol_rel and an absolute tolerance xtol_abs<sub>*i*</sub> on the parameters **x**. Again, it is practically impossible for these to be tolerances on the actual error Δ**x** compared to the (unknown) minimum point, so in practice Δ**x** is usually some measure of how much **x** changes by from one iteration to the next, or the diameter of a search region, or something like that. Then the algorithm stops when either |Δ*x*<sub>*i*</sub>| < xtol_abs<sub>*i*</sub> or when |Δ*x*<sub>*i*</sub>|/|*x*<sub>*i*</sub>| < xtol_rel. However, there is some variation in how the different algorithms implement **x** tolerance tests; for example, some of them check instead whether |Δ**x**|/|**x**| < xtol_rel, where |•| is some norm.
+
+- <b>Note:</b> generally, you can only ask for about *half* as many decimal places in the xtol as in the ftol. The reason is that, near the minimum, $\Delta f \approx f'' (\Delta x)^2 / 2$ from the [Taylor expansion](https://en.wikipedia.org/wiki/Taylor_expansion), and so (assuming $f'' \approx 1$ for simplicity) a change in *x* by 10<sup>–7</sup> gives a change in *f* by around 10<sup>–14</sup>. In particular, this means that it is generally hopeless to request an xtol_rel much smaller than the *square root* of [machine precision](https://en.wikipedia.org/wiki/Machine_epsilon).
+
+In most cases, the fractional tolerance (tol_rel) is the most useful one to specify, because it is independent of any absolute scale factors or units. Absolute tolerance (tol_abs) is mainly useful if you think that the minimum function value or parameters might occur at or close to zero.
+
+If you don't want to use a particular tolerance termination, you can just set that tolerance to zero and it will be ignored.
+
+### Stopping function value
+
+Another termination test that NLopt supports is that you can tell the optimization to stop when the objective function value *f*(**x**) reaches some specified value, `stopval`, for any feasible point **x**.
+
+This termination test is especially useful when [comparing algorithms](NLopt_Algorithms#Comparing_algorithms.md) for a given problem. After running one algorithm for a long time to find the minimum to the desired accuracy, you can ask how many iterations algorithms require to obtain the optimum to the same accuracy or to some better accuracy.
+
+### Bounds on function evaluations and wall-clock time
+
+Finally, one can also set a termination condition by specifying a maximum number of function evaluations (maxeval) or a maximum [wall-clock time](https://en.wikipedia.org/wiki/Wall_clock_time) (maxtime). That is, the simulation terminates when the number of function evaluations reaches maxeval, or when the total elapsed time exceeds some specified maxtime.
+
+These termination conditions are useful if you want to ensure that the algorithm gives you *some* answer in a reasonable amount of time, even if it is not absolutely optimal, and are also useful ways to control global optimization.
+
+Note that these are only rough maximums; a given algorithm may exceed the specified maximum time or number of function evaluations slightly.
+
+### Termination tests for global optimization
+
+In general, deciding when to terminate a global optimization algorithm is a rather difficult problem, because there is no way to be certain (without special information about a particular *f*) that you have truly reached the global minimum, or even come close. You never know when there might be a much smaller value of the objective function lurking in some tiny corner of the feasible region.
+
+Because of this, the most reasonable termination criterion for global optimization problems seems to be setting bounds on the run time. That is, set an upper bound on how long you are willing to wait for an answer, and use that as the maximum run time. Another strategy is to start with a shorter run time, and repeatedly double the run time until the answer stops changing to your satisfaction. (Although there can be no guarantee that increasing the time further won't lead to a much better answer, there's not much you can do about it.)
+
+I would advise you *not* to use function-value (ftol) or parameter tolerances (xtol) in global optimization. I made a half-hearted attempt to implement these tests in the various global-optimization algorithms, but it doesn't seem like there is any really satisfactory way to go about this, and I can't claim that my choices were especially compelling.
+
+For the [MLSL](NLopt_Algorithms#MLSL_(Multi-Level_Single-Linkage).md) algorithm, you need to set the ftol and xtol [parameters of the local optimization algorithm](NLopt_Reference#Local/subsidiary_optimization_algorithm.md) control the tolerances of the *local* searches, *not* of the global search; you should definitely set these, lest the algorithm spend an excessive amount of time trying to run local searches to machine precision.
+
+Background and goals of NLopt
+-----------------------------
+
+NLopt was started because some of the students in our group needed to use an optimization algorithm for a nonlinear problem, but it wasn't clear which algorithm would work best (or work at all). One student started by downloading one implementation from the Web, figuring out how to plug it into her Matlab program, getting it to work, only to find that it didn't converge very quickly so she needed another one, and so on... Then another student went through the same process, only his program was in C and he needed to get the algorithms to work with that language, and he obtained a different set of algorithms. It quickly became apparent that the duplication of effort was untenable, and the considerable labor required to decipher each new subroutine, figure out how to build it, figure out how to bridge the gap from one language (e.g. Fortran) to another (e.g. Matlab or C), and so on, was so substantial that it was hard to justify trying more than one or two. Even though the first two algorithms tried might converge poorly, or might be severely limited in the types of constraints they could handle, or have other limitations, effective experimentation was impractical.
+
+Instead, since I had some experience in wrapping C and Fortran routines and making them callable from C and Matlab and other languages, it made sense to put together a common wrapper interface for a few of the more promising of the free/open-source subroutines I could find online. Soon, it became clear that I wanted at least one decent algorithm in each major category (constrained/unconstrained, global/local, gradient-based/derivative-free, bound/nonlinear constraints), but there wasn't always free code available. Reading the literature turned up tantalizing hints of algorithms that were claimed to be very powerful, but again had no free code. And some algorithms had free code, but only in a language like Matlab that was impractical to use in stand-alone fashion from C. So, in addition to wrapping existing code, I began to write my own implementations of various algorithms that struck my interest or seemed to fill a need.
+
+Initially, my plan was to handle only bound constraints, and leave general nonlinear constraints to others—who needs such things? That attitude lasted until we found that we needed to solve a 10,000-dimensional minimax-type problem, which seemed intractable unless gradient-based algorithms could be brought to bear...as discussed above, this requires nonlinear constraints to make the problem differentiable. After some reading, I came across the MMA algorithm, which turned out to be easy to implement (300 lines of C), and worked beautifully (at least for my problem), so I expanded the NLopt interface to support nonlinear constraints.
+
+Overall, I've found that this has been surprisingly fun. Every once in a while, I come across a new algorithm to try, and now that I've implemented a few algorithms and built up a certain amount of infrastructure, it is relatively easy to add new ones (much more so than when I first started out). So, I expect that NLopt will continue to grow, albeit perhaps more slowly now that it seems to include decent algorithms for a wide variety of problems.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt License and Copyright
+---
+
+The NLopt library is under the [GNU Lesser General Public License](https://en.wikipedia.org/wiki/GNU_Lesser_General_Public_License) (LGPL), and the copyrights are owned by a variety of authors.
+
+In general, the different code in NLopt comes from different sources, and have a variety of licenses. For example, all of the *new* code we wrote for NLopt is under the [MIT License](https://en.wikipedia.org/wiki/MIT_License) (which imposes essentially no practical restrictions, and is hence compatible with the LGPL). The *combination* of all of this software is under the conjunction of the license terms, and in particular they are limited by the most restrictive of the licenses for the portions, which in this case is the LGPL. (The other portions of NLopt are under LGPL-compatible, less-restrictive licenses like the MIT license. So, if you remove the LGPL portions, which are currently code [by Ladislav Luksan](http://www.uivt.cas.cz/~luksan/subroutines.html), the remainder reverts to a looser license.)
+
+New code written by me for NLopt, including tutorial code at [NLopt Tutorial](NLopt_Tutorial.md), is Copyright © 2007-2010 Massachusetts Institute of Technology, and comes with **no warranty**:
+
+**THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.**
+
+Please [cite NLopt](Citing_NLopt.md) and the authors of the respective algorithms in any publication for which you find it useful. (This is not a legal requirement, just a polite request.)
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt Matlab Reference
+---
+
+The NLopt includes interfaces callable from the [Matlab](https://en.wikipedia.org/wiki/MATLAB) and [GNU Octave](https://en.wikipedia.org/wiki/GNU_Octave) (a free-software Matlab-like program), using identical syntax.
+
+The main purpose of this section is to document the syntax and unique features of the Matlab API; for more detail on the underlying features, please refer to the C documentation in the [NLopt Reference](NLopt_Reference.md).
+
+Using the NLopt Matlab API
+--------------------------
+
+On Unix, the Matlab and Octave interfaces should automatically be installed in places where they will be found at runtime, assuming you have Matlab and Octave correctly installed on your machine, as documented in the [Installation manual](NLopt_Installation.md).
+
+On Windows, we provide a precompiled [.zip](https://en.wikipedia.org/wiki/.zip) file of the NLopt library, which includes a `matlab` directory. In this directory are a set of `.m` files (mostly implementing constants and documentation) and a `nlopt-optimize.c` file which can be compiled into a [w:MEX file](https://en.wikipedia.org/wiki/MEX_file) callable from Matlab. All of these files must be placed somewhere in your Matlab path or in your working directory if you want to use them.
+
+The `opt` structure
+-------------------
+
+The NLopt API revolves around an [Matlab structure](http://www.mathworks.com/access/helpdesk/help/techdoc/matlab_prog/f2-88951.html), analogous to the `nlopt_opt` object in C and similar objects in NLopt's interfaces for other languages. All of the parameters of the optimization are specified (dimensions, algorithm, stopping criteria, constraints, objective function, etcetera) simply by assigning fields to this structure, and then one finally calls the `nlopt_optimize(opt)` function in order to perform the optimization. Every `opt` structure should specify the algorithm, via:
+
+`opt.algorithm = `*`algorithm`*
+
+given an *`algorithm`* (see [NLopt Algorithms](NLopt_Algorithms.md) for possible values) and the dimensionality of the problem (`n`, the number of optimization parameters). Just as in C, algorithms are specified by predefined constants of the form `NLOPT_MMA`, `NLOPT_COBYLA`, etcetera.
+
+*You need not set all the fields* of the structure; any fields that are not specified take on innocuous default values (the same as if you did not specify those parameters in the C interface).
+
+The dimension *n* of the problem (the number of optimization parameters) is determined implicitly by the length of the vector you pass to `nlopt_optimize` as the initial guess. An error will occur if you use vectors of inconsistent lengths (e.g. you set `opt.lower_bounds` to be a different length).
+
+Objective function
+------------------
+
+The objective function is specified setting either the `opt.min_objective` or `opt.max_objective` field to a [function handle](http://www.mathworks.com/access/helpdesk/help/techdoc/ref/function_handle.html) for the objective function *f*, depending on whether one wishes to minimize or maximize `f`, respectively. The function `f` should be of the form:
+
+```
+function [val, gradient] = myfunc(x)
+```
+
+` val = `*`...value` `of` `f(x)...`*
+```
+ if (nargout > 1)
+```
+
+` gradient = `*`...gradient` `at` `x...`*
+```
+ end
+```
+
+
+The first return value should be the value of the function at the point `x`, where `x` row or column vector of the `n` of the *n* optimization parameters (the same length as the initial guess passed to `nlopt_optimize`). (Whether `x` is a row or column vector depends on whether the initial guess you pass to `nlopt_optimize` is a row or column vector, respectively.)
+
+In addition, if the caller requests two return values (`nargout` `>` `1`), then the second return value `gradient` should be a vector (row or column) of length `n` that is the gradient of the function with respect to the optimization parameters at `x`. That is, `grad(i)` should upon return contain the partial derivative $\partial f / \partial x_i$, for $1 < i \leq n$. Not all of the optimization algorithms (below) use the gradient information: for algorithms listed as "derivative-free," the `nargout` will always be 1 and the gradient need never be computed.
+
+If your objective function returns [NaN](https://en.wikipedia.org/wiki/NaN) (`nan` in Matlab), that will force the optimization to terminate, equivalent to calling [nlopt_force_stop](NLopt_Reference#Forced_termination.md) in C.
+
+Bound constraints
+-----------------
+
+The [bound constraints](NLopt_Reference#Bound_constraints.md) can be specified by setting `opt.lower_bounds` and/or `opt.upper_bounds` to vectors of length *n* (the same as the length of the initial guess passed to `nlopt_optimize`).
+
+To specify an unbounded dimension, you can use ±`inf` in Matlab to specify ±∞.
+
+Nonlinear constraints
+---------------------
+
+Just as for [nonlinear constraints in C](NLopt_Reference#Nonlinear_constraints.md), you can specify nonlinear inequality and equality constraints by setting `opt.fc` and `opt.h` to be [cell arrays](http://blogs.mathworks.com/loren/2006/06/21/cell-arrays-and-their-contents/) of function handles (of the same form as the objective function above) for the inequality and equality constraints, respectively.
+
+Recall that a cell array is specified via `{...}` in Matlab, e.g. `{` `@constraint1,` `@constraint2` `}`.
+
+Optionally, you can specify a tolerance in judging feasibility for the purposes of stopping the optimization, as in C. Tolerances are specified as fields `opt.fc_tol` and `opt.h_tol`, which (if they are set) should be vectors (not cell arrays) of tolerances, of the same lengths as `opt.fc` and `opt.h`, respectively. (If they are not specified, the tolerances default to zero.)
+
+Stopping criteria
+-----------------
+
+As explained in the [C API Reference](NLopt_Reference#Stopping_criteria.md) and the [Introduction](NLopt_Introduction#Termination_conditions.md)), you have multiple options for different stopping criteria that you can specify. (Unspecified stopping criteria are disabled; i.e., they have innocuous defaults.) The various stopping criteria can be specified via the following fields of your structure.
+
+```
+opt.stopval
+```
+
+
+Stop when an objective value of at least `stopval` is found.
+
+```
+opt.ftol_rel
+```
+
+
+Set relative tolerance on function value.
+
+```
+opt.ftol_abs
+```
+
+
+Set absolute tolerance on function value.
+
+```
+opt.xtol_rel
+```
+
+
+Set relative tolerance on optimization parameters.
+
+```
+opt.xtol_abs
+```
+
+
+Set absolute tolerances on optimization parameters. The `opt.xtol_abs` value must be a vector of length `n` (the same length as the initial guess passed to `nlopt_optimize`) of the tolerances.
+
+```
+opt.maxeval
+```
+
+
+Stop when the number of function evaluations exceeds `maxeval`. (0 or negative for no limit.) An integer.
+
+```
+opt.maxtime
+```
+
+
+Stop when the optimization time (in seconds) exceeds `maxtime`. (0 or negative for no limit.)
+
+Performing the optimization
+---------------------------
+
+Once all of the desired optimization parameters have been specified in a given structure `opt`, you can perform the optimization by calling:
+
+```
+[xopt, fmin, retcode] = nlopt_optimize(opt, x);
+```
+
+
+On input, `x` is a vector (row or column) of length `n` (this specifies the dimension of the problem, and must be consistent with vectors you use elsewhere as mentioned above) giving an initial guess for the optimization parameters. The return value `xopt` is a vector (row or column, same as `x`) containing the optimized values of the optimization parameters.
+
+The second return value `fmin` is the optimized value of the objective function, and the third value is a return code (negative on failure and positive on success).
+
+Local/subsidiary optimization algorithm
+---------------------------------------
+
+Some of the algorithms, especially MLSL and AUGLAG, use a different optimization algorithm as a subroutine, typically for local optimization. You can change the local search algorithm and its tolerances by setting the `opt.local_optimizer` field to *another* optimization structure.
+
+For example, `opt.local_optimizer.algorithm` `=` `NLOPT_LN_BOBYQA;` `opt.local_optimizer.ftol_rel` `=` `1e-4` will set the local optimizer to use BOBYQA and a relative function tolerance of `1e-4`.
+
+The fields of `opt.local_optimizer` are used to determine the local search algorithm, its stopping criteria, and other algorithm parameters. (However, the objective function, bounds, and nonlinear-constraint parameters of `opt.local_optimizer` are ignored.)
+
+Initial step size
+-----------------
+
+Just as in the C API, you can [get and set the initial step sizes](NLopt_Reference#Initial_step_size.md) for derivative-free optimization algorithms. In Matlab, you set the `opt.initial_step` field to a vector of the (nonzero) initial steps for each dimension.
+
+Stochastic population
+---------------------
+
+Just as in the C API, you can [get and set the initial population](NLopt_Reference#Stochastic_population.md) for stochastic optimization algorithms, by setting `opt.population` to an (integer) initial population. (An `opt.population` of zero implies that the heuristic default will be used.)
+
+Vector storage for limited-memory quasi-Newton algorithms
+---------------------------------------------------------
+
+Just as in the C API, you can set the [number *M* of stored vectors for limited-memory quasi-Newton algorithms](NLopt_Reference#Vector_storage_for_limited-memory_quasi-Newton_algorithms.md), via:
+
+```
+opt.vector_storage
+```
+
+
+(The default is 0, in which case NLopt uses a heuristic nonzero value.)
+
+Verbose output
+--------------
+
+If you set `opt.verbose` to `1`, the Matlab interface will output information as the optimization progresses, such as the objective function values.
+
+Of course, your objective function and constraints can also output anything you wish, using `disp` and similar Matlab functions.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt Python Reference
+---
+
+The NLopt includes an interface callable from the [Python programming language](https://en.wikipedia.org/wiki/Python_(programming_language)).
+
+The main purpose of this section is to document the syntax and unique features of the Python API; for more detail on the underlying features, please refer to the C documentation in the [NLopt Reference](NLopt_Reference.md).
+
+Using the NLopt Python API
+--------------------------
+
+To use NLopt in Python, your Python program should include the lines:
+
+```
+import nlopt
+from numpy import *
+```
+
+
+which imports the `nlopt` module, and also imports the numpy ([NumPy](https://en.wikipedia.org/wiki/NumPy)) that defines the array data types used for communicating with NLopt.
+
+The `nlopt.opt` class
+---------------------
+
+The NLopt API revolves around an object of type `nlopt.opt`. Via methods of this object, all of the parameters of the optimization are specified (dimensions, algorithm, stopping criteria, constraints, objective function, etcetera), and then one finally calls the `opt.optimize` method in order to perform the optimization. The object should normally be created via the constructor:
+
+```
+opt = nlopt.opt(algorithm, n)
+```
+
+
+given an `algorithm` (see [NLopt Algorithms](NLopt_Algorithms.md) for possible values) and the dimensionality of the problem (`n`, the number of optimization parameters). Whereas the C algorithms are specified by `nlopt_algorithm` constants of the form `NLOPT_LD_MMA`, `NLOPT_LN_COBYLA`, etcetera, the Python `algorithm` values are of the form `nlopt.LD_MMA`, `nlopt.LN_COBYLA`, etcetera (with the `NLOPT_` prefix replaced by the `nlopt.` namespace).
+
+There are also a copy constructor `nlopt.opt(opt)` to make a copy of a given object (equivalent to `nlopt_copy` in the C API).
+
+If there is an error in the constructor (or copy constructor, or assignment), a `MemoryError` exception is thrown.
+
+The algorithm and dimension parameters of the object are immutable (cannot be changed without constructing a new object), but you can query them for a given object by the methods:
+
+```
+opt.get_algorithm()
+opt.get_dimension()
+```
+
+
+You can get a string description of the algorithm via:
+
+```
+opt.get_algorithm_name()
+```
+
+
+Objective function
+------------------
+
+The objective function is specified by calling one of the methods:
+
+```
+opt.set_min_objective(f)
+opt.set_max_objective(f)
+```
+
+
+depending on whether one wishes to minimize or maximize the objective function `f`, respectively. The function `f` should be of the form:
+
+```
+def f(x, grad):
+ if grad.size > 0:
+```
+
+` `*`...set` `grad` `to` `gradient,` `in-place...`*
+` return `*`...value` `of` `f(x)...`*
+
+The return value should be the value of the function at the point `x`, where `x` is a NumPy array of length `n` of the optimization parameters (the same as the dimension passed to the constructor).
+
+In addition, if the argument `grad` is not empty $$i.e. `grad.size>0`$$, then `grad` is a NumPy array of length `n` which should (upon return) be set to the gradient of the function with respect to the optimization parameters at `x`. That is, `grad[i]` should upon return contain the partial derivative $\partial f / \partial x_i$, for $0 \leq i < n$, if `grad` is non-empty. Not all of the optimization algorithms (below) use the gradient information: for algorithms listed as "derivative-free," the `grad` argument will always be empty and need never be computed. (For algorithms that do use gradient information, however, `grad` may still be empty for some calls.)
+
+Note that `grad` must be modified *in-place* by your function `f`. Generally, this means using indexing operations `grad[...]` `=` `...` to overwrite the contents of `grad`, as described below.
+
+### Assigning results in-place
+
+Your objective and constraint functions must overwrite the contents of the `grad` (gradient) argument in-place (although of course you can allocate whatever additional storage you might need, in addition to overwriting `grad`). However, typical Python assignment operations do *not* do this. For example:
+
+```
+grad = 2*x
+```
+
+
+might seem like the gradient of the function `sum(x**2)`, but it will *not work* with NLopt because this expression actually allocates a *new* array to store `2*x` and re-assigns `grad` to point to it, rather than overwriting the old contents of `grad`. Instead, you should do:
+
+```
+grad[:] = 2*x
+```
+
+
+Assigning any [slice or view](http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html) `grad[...]` of the array will overwrite the contents, which is what NLopt needs you to do. So, you should generally use indexing expressions `grad[...]` `=` `...` to assign the gradient result.
+
+In specific cases, there are a few other NumPy and SciPy functions that are documented to operate in-place on their arguments, and you can also use such functions to modify `grad` if you want. If a function is not *explicitly documented to modify its arguments in-place*, however, you should assume that it does *not*.
+
+Bound constraints
+-----------------
+
+The [bound constraints](NLopt_Reference#Bound_constraints.md) can be specified by calling the methods:
+
+```
+opt.set_lower_bounds(lb)
+opt.set_upper_bounds(ub)
+```
+
+
+where `lb` and `ub` are arrays (NumPy arrays or Python lists) of length *n* (the same as the dimension passed to the `nlopt.opt` constructor). For convenience, these are overloaded with functions that take a single number as arguments, in order to set the lower/upper bounds for all optimization parameters to a single constant.
+
+To retrieve the values of the lower/upper bounds, you can call one of:
+
+```
+opt.get_lower_bounds()
+opt.get_upper_bounds()
+```
+
+
+both of which return NumPy arrays.
+
+To specify an unbounded dimension, you can use ±`float('inf')` (or ±`numpy.inf`) in Python to specify ±∞.
+
+Nonlinear constraints
+---------------------
+
+Just as for [nonlinear constraints in C](NLopt_Reference#Nonlinear_constraints.md), you can specify nonlinear inequality and equality constraints by the methods:
+
+```
+opt.add_inequality_constraint(fc, tol=0)
+opt.add_equality_constraint(h, tol=0)
+```
+
+
+where the arguments `fc` and `h` have the same form as the objective function above. The optional `tol` arguments specify a tolerance in judging feasibility for the purposes of stopping the optimization, as in C.
+
+To remove all of the inequality and/or equality constraints from a given problem, you can call the following methods:
+
+```
+opt.remove_inequality_constraints()
+opt.remove_equality_constraints()
+```
+
+
+### Vector-valued constraints
+
+Just as for [nonlinear constraints in C](NLopt_Reference#Vector-valued_constraints.md), you can specify vector-valued nonlinear inequality and equality constraints by the methods
+
+```
+opt.add_inequality_mconstraint(c, tol)
+opt.add_inequality_mconstraint(c, tol)
+```
+
+
+Here, `tol` is an array (NumPy array or Python list) of the tolerances in each constraint dimension; the dimensionality *m* of the constraint is determined by `tol.size`. The constraint function `c` must be of the form:
+
+```
+def c(result, x, grad):
+ if grad.size > 0:
+```
+
+` `*`...set` `grad` `to` `gradient,` `in-place...`*
+` result[0] = `*`...value` `of` `c`<sub>`0`</sub>`(x)...`*
+` result[1] = `*`...value` `of` `c`<sub>`1`</sub>`(x)...`*
+```
+ ...
+```
+
+
+`result` is a NumPy array whose length equals the dimensionality *m* of the constraint (same as the length of `tol` above), which upon return should be set *in-place* ([see above](#Assigning_results_in-place.md)) to the constraint results at the point `x` (a NumPy array whose length *n* is the same as the dimension passed to the constructor). Any return value of the function is ignored.
+
+In addition, if the argument `grad` is not empty $$i.e. `grad.size>0`$$, then `grad` is a 2d NumPy array of size *m*×*n* which should (upon return) be set in-place ([see above](#Assigning_results_in-place.md)) to the gradient of the function with respect to the optimization parameters at `x`. That is, `grad[i,j]` should upon return contain the partial derivative $\partial c_i / \partial x_j$ if `grad` is non-empty. Not all of the optimization algorithms (below) use the gradient information: for algorithms listed as "derivative-free," the `grad` argument will always be empty and need never be computed. (For algorithms that do use gradient information, however, `grad` may still be empty for some calls.)
+
+An inequality constraint corresponds to $c_i \le 0$ for $0 \le i < m$, and an equality constraint corresponds to $c_i = 0$, in both cases with tolerance `tol[i]` for purposes of termination criteria.
+
+(You can add multiple vector-valued constraints and/or scalar constraints in the same problem.)
+
+Stopping criteria
+-----------------
+
+As explained in the [C API Reference](NLopt_Reference#Stopping_criteria.md) and the [Introduction](NLopt_Introduction#Termination_conditions.md)), you have multiple options for different stopping criteria that you can specify. (Unspecified stopping criteria are disabled; i.e., they have innocuous defaults.)
+
+For each stopping criteria, there are (at least) two methods: a `set` method to specify the stopping criterion, and a `get` method to retrieve the current value for that criterion. The meanings of each criterion are exactly the same as in the C API.
+
+```
+opt.set_stopval(stopval)
+opt.get_stopval()
+```
+
+
+Stop when an objective value of at least `stopval` is found.
+
+```
+opt.set_ftol_rel(tol)
+opt.get_ftol_rel()
+```
+
+
+Set relative tolerance on function value.
+
+```
+opt.set_ftol_abs(tol)
+opt.get_ftol_abs()
+```
+
+
+Set absolute tolerance on function value.
+
+```
+opt.set_xtol_rel(tol)
+opt.get_xtol_rel()
+```
+
+
+Set relative tolerance on optimization parameters.
+
+```
+opt.set_xtol_abs(tol)
+opt.get_xtol_abs()
+```
+
+
+Set absolute tolerances on optimization parameters. The `tol` input must be an array (NumPy array or Python list) of length `n` (the dimension specified in the `nlopt.opt` constructor); alternatively, you can pass a single number in order to set the same tolerance for all optimization parameters. `get_xtol_abs()` returns the tolerances as a NumPy array.
+
+```
+opt.set_maxeval(maxeval)
+opt.get_maxeval()
+```
+
+
+Stop when the number of function evaluations exceeds `maxeval`. (0 or negative for no limit.)
+
+```
+opt.set_maxtime(maxtime)
+opt.get_maxtime()
+```
+
+
+Stop when the optimization time (in seconds) exceeds `maxtime`. (0 or negative for no limit.)
+
+### Forced termination
+
+In certain cases, the caller may wish to *force* the optimization to halt, for some reason unknown to NLopt. For example, if the user presses Ctrl-C, or there is an error of some sort in the objective function. You can do this by raise *any* exception inside your objective/constraint functions:the optimization will be halted gracefully, and the same exception will be raised to the caller. See [Exceptions](#Exceptions.md), below. The Python equivalent of `nlopt_forced_stop` from the [C API](NLopt_Reference#Forced_termination.md) is to throw an `nlopt.ForcedStop` exception.
+
+Performing the optimization
+---------------------------
+
+Once all of the desired optimization parameters have been specified in a given object `opt`, you can perform the optimization by calling:
+
+```
+xopt = opt.optimize(x)
+```
+
+
+On input, `x` is an array (NumPy array or Python list) of length `n` (the dimension of the problem from the `nlopt.opt` constructor) giving an initial guess for the optimization parameters. The return value `xopt` is a NumPy array containing the optimized values of the optimization parameters.
+
+You can call the following methods to retrieve the optimized objective function value from the last `optimize` call, and also the return code (including negative/failure return values) from the last `optimize` call:
+
+```
+opt_val = opt.last_optimum_value()
+result = opt.last_optimize_result()
+```
+
+
+The return code (see below) is positive on success, indicating the reason for termination. On failure (negative return codes), `optimize()` throws an exception (see [Exceptions](#Exceptions.md), below).
+
+### Return values
+
+The possible return values are the same as the [return values in the C API](NLopt_Reference#Return_values.md), except that the `NLOPT_` prefix is replaced with the `nlopt.` namespace. That is, `NLOPT_SUCCESS` becomes `nlopt.SUCCESS`, etcetera.
+
+Exceptions
+----------
+
+The [Error codes (negative return values)](NLopt_Reference#Error_codes_(negative_return_values).md) in the C API are replaced in the Python API by thrown exceptions. The following exceptions are thrown by the various routines:
+
+```
+RunTimeError
+```
+
+Generic failure, equivalent to `NLOPT_FAILURE`.
+
+```
+ValueError
+```
+
+Invalid arguments (e.g. lower bounds are bigger than upper bounds, an unknown algorithm was specified, etcetera), equivalent to `NLOPT_INVALID_ARGS`.
+
+```
+MemoryError
+```
+
+Ran out of memory (a memory allocation failed), equivalent to `NLOPT_OUT_OF_MEMORY`.
+
+`nlopt.RoundoffLimited` (subclass of `Exception`)
+Halted because roundoff errors limited progress, equivalent to `NLOPT_ROUNDOFF_LIMITED`.
+
+`nlopt.ForcedStop` (subclass of `Exception`)
+Halted because of a [forced termination](#Forced_termination.md): the user called `opt.force_stop()` from the user’s objective function or threw an `nlopt.ForcedStop` exception. Equivalent to `NLOPT_FORCED_STOP`.
+
+If your objective/constraint functions throw *any* exception during the execution of `opt.optimize`, it will be caught by NLopt and the optimization will be halted gracefully, and `opt.optimize` will re-throw the *same* exception to its caller.
+
+Local/subsidiary optimization algorithm
+---------------------------------------
+
+Some of the algorithms, especially MLSL and AUGLAG, use a different optimization algorithm as a subroutine, typically for local optimization. You can change the local search algorithm and its tolerances by calling:
+
+```
+opt.set_local_optimizer(local_opt)
+```
+
+
+Here, `local_opt` is another `nlopt.opt` object whose parameters are used to determine the local search algorithm, its stopping criteria, and other algorithm parameters. (However, the objective function, bounds, and nonlinear-constraint parameters of `local_opt` are ignored.) The dimension `n` of `local_opt` must match that of `opt`.
+
+This function makes a copy of the `local_opt` object, so you can freely change your original `local_opt` afterwards without affecting `opt`.
+
+Initial step size
+-----------------
+
+Just as in the C API, you can [get and set the initial step sizes](NLopt_Reference#Initial_step_size.md) for derivative-free optimization algorithms. The Python equivalents of the C functions are the following methods:
+
+```
+opt.set_initial_step(dx)
+opt.get_initial_step(x)
+```
+
+
+Here, `dx` is an array (NumPy array or Python list) of the (nonzero) initial steps for each dimension, or a single number if you wish to use the same initial steps for all dimensions. `opt.get_initial_step(x)` returns the initial step that will be used for a starting guess of `x` in `opt.optimize(x)`.
+
+Stochastic population
+---------------------
+
+Just as in the C API, you can [get and set the initial population](NLopt_Reference#Stochastic_population.md) for stochastic optimization algorithms, by the methods:
+
+```
+opt.set_population(pop)
+opt.get_population()
+```
+
+
+(A `pop` of zero implies that the heuristic default will be used.)
+
+Pseudorandom numbers
+--------------------
+
+For stochastic optimization algorithms, we use pseudorandom numbers generated by the [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_twister) algorithm, based on code from Makoto Matsumoto. By default, the [seed](https://en.wikipedia.org/wiki/Random_seed) for the random numbers is generated from the system time, so that you will get a different sequence of pseudorandom numbers each time you run your program. If you want to use a "deterministic" sequence of pseudorandom numbers, i.e. the same sequence from run to run, you can set the seed by calling:
+
+```
+nlopt.srand(seed)
+```
+
+
+where `seed` is an integer. To reset the seed based on the system time, you can call:
+
+```
+nlopt.srand_time()
+```
+
+
+(Normally, you don't need to call this as it is called automatically. However, it might be useful if you want to "re-randomize" the pseudorandom numbers after calling `nlopt.srand` to set a deterministic seed.)
+
+Vector storage for limited-memory quasi-Newton algorithms
+---------------------------------------------------------
+
+Just as in the C API, you can get and set the [number *M* of stored vectors](NLopt_Reference#Vector_storage_for_limited-memory_quasi-Newton_algorithms.md) for limited-memory quasi-Newton algorithms, via the methods:
+
+```
+opt.set_vector_storage(M)
+opt.get_vector_storage()
+```
+
+
+(The default is *M*=0, in which case NLopt uses a heuristic nonzero value.)
+
+Version number
+--------------
+
+To determine the version number of NLopt at runtime, you can call:
+
+```
+nlopt.version_major()
+nlopt.version_minor()
+nlopt.version_bugfix()
+```
+
+
+For example, NLopt version 3.1.4 would return `major=3`, `minor=1`, and `bugfix=4`.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt R Reference
+---
+
+An NLopt interface for [GNU R](https://en.wikipedia.org/wiki/GNU_R) was developed by [Jelmer Ypma](http://www.ucl.ac.uk/~uctpjyy) at [University College London](https://en.wikipedia.org/wiki/University_College_London) (UCL), and is currently available as a separate download (with documentation) from:
+
+- [<http://www.ucl.ac.uk/~uctpjyy/nloptr.html>](http://www.ucl.ac.uk/~uctpjyy/nloptr.html)
--- /dev/null
+---
+# NLopt Reference
+---
+
+NLopt is a library, not a stand-alone program—it is designed to be called from your own program in C, C++, Fortran, Matlab, GNU Octave, or other languages. This reference section describes the programming interface (API) of NLopt in the C language. The reference manuals for other languages can be found at:
+
+- [NLopt C++ Reference](NLopt_C-plus-plus_Reference.md)
+- [NLopt Fortran Reference](NLopt_Fortran_Reference.md)
+- [NLopt Matlab Reference](NLopt_Matlab_Reference.md)
+- [NLopt Python Reference](NLopt_Python_Reference.md)
+- [NLopt Guile Reference](NLopt_Guile_Reference.md)
+- [NLopt Julia Reference](https://github.com/stevengj/NLopt.jl)
+
+The old API from versions of NLopt prior to 2.0 is deprecated, but continues to be supported for backwards compatibility. You can find it described in the [NLopt Deprecated API Reference](NLopt_Deprecated_API_Reference.md).
+
+Other sources of information include the Unix [man page](https://en.wikipedia.org/wiki/Manual_page_(Unix)): On Unix, you can run e.g. `man` `nlopt` for documentation of C API. In Matlab and GNU Octave, the corresponding command is to type `help` `nlopt_optimize`.
+
+Compiling and linking your program to NLopt
+-------------------------------------------
+
+An NLopt program in C should include the NLopt header file:
+
+`#include `<nlopt.h>
+
+For programs in compiled languages like C or Fortran, when you compile your program you will have to link it to the NLopt library. This is *in addition* to including the header file (`#include` <nlopt.h> in C or `#include` <nlopt.hpp> in C++). On Unix, you would normally link with a command something like:
+
+*`compiler`*` `*`...source/object` `files...`*` -lnlopt -lm -o myprogram`
+
+where *compiler* is `cc`, `f77`, `g++`, or whatever is appropriate for your machine/language.
+
+*Note:* the `-lnlopt` `-lm` options, which link to the NLopt library (and the math library, which it requires), must come *after* your source/object files. In general, the rule is that if *A* depends upon *B*, then *A* must come before *B* in the link command.
+
+*Note:* the above example assumes that you have installed the NLopt library in a place where the compiler knows to find it (e.g. in a standard directory like `/usr/lib` or `/usr/local/lib`). If you installed somewhere else (e.g. in your home directory if you are not a system administrator), then you will need to use a `-L` flag to tell the compiler where to find the library. See [the installation manual](NLopt_Installation#Changing_the_installation_directory.md).
+
+The `nlopt_opt` object
+----------------------
+
+The NLopt API revolves around an "object" of type `nlopt_opt` (an opaque pointer type). Via this object, all of the parameters of the optimization are specified (dimensions, algorithm, stopping criteria, constraints, objective function, etcetera), and then one finally passes this object to `nlopt_optimize` in order to perform the optimization. The object is created by calling:
+
+```
+nlopt_opt nlopt_create(nlopt_algorithm algorithm, unsigned n);
+```
+
+
+which returns a newly allocated `nlopt_opt` object (or NULL if there was an error, e.g. out of memory), given an `algorithm` (see [NLopt Algorithms](NLopt_Algorithms.md) for possible values) and the dimensionality of the problem (`n`, the number of optimization parameters).
+
+When you are finished with the object, you must deallocate it by calling:
+
+```
+void nlopt_destroy(nlopt_opt opt);
+```
+
+
+Simple assignment (`=`) makes two pointers to the same object. To make an independent copy of an object, use:
+
+```
+nlopt_opt nlopt_copy(const nlopt_opt opt);
+```
+
+
+The algorithm and dimension parameters of the object are immutable (cannot be changed without creating a new object), but you can query them for a given object by calling:
+
+```
+nlopt_algorithm nlopt_get_algorithm(const nlopt_opt opt);
+unsigned nlopt_get_dimension(const nlopt_opt opt);
+```
+
+
+You can get a descriptive (null-terminated) string corresponding to a particular algorithm by calling:
+
+```
+const char *nlopt_algorithm_name(nlopt_algorithm algorithm);
+```
+
+
+Objective function
+------------------
+
+The objective function is specified by calling one of:
+
+```
+nlopt_result nlopt_set_min_objective(nlopt_opt opt, nlopt_func f, void* f_data);
+nlopt_result nlopt_set_max_objective(nlopt_opt opt, nlopt_func f, void* f_data);
+```
+
+
+depending on whether one wishes to minimize or maximize the objective function `f`, respectively. The function `f` should be of the form:
+
+```
+ double f(unsigned n, const double* x, double* grad, void* f_data);
+```
+
+
+The return value should be the value of the function at the point `x`, where `x` points to an array of length `n` of the optimization parameters. The dimension `n` is identical to the one passed to `nlopt_create`.
+
+In addition, if the argument `grad` is not `NULL`, then `grad` points to an array of length `n` which should (upon return) be set to the gradient of the function with respect to the optimization parameters at `x`. That is, `grad[i]` should upon return contain the partial derivative $\partial f / \partial x_i$, for $0 \leq i < n$, if `grad` is non-`NULL`. Not all of the optimization algorithms (below) use the gradient information: for algorithms listed as "derivative-free," the `grad` argument will always be `NULL` and need never be computed. (For algorithms that do use gradient information, however, `grad` may still be `NULL` for some calls.)
+
+The `f_data` argument is the same as the one passed to `nlopt_set_min_objective` or `nlopt_set_max_objective`, and may be used to pass any additional data through to the function. (That is, it may be a pointer to some caller-defined data structure/type containing information your function needs, which you convert from `void*` by a typecast.)
+
+Bound constraints
+-----------------
+
+Most of the algorithms in NLopt are designed for minimization of functions with simple bound constraints on the inputs. That is, the input vectors `x[i]` are constrainted to lie in a hyperrectangle `lb[i]` ≤ `x[i]` ≤ `ub[i]` for 0 ≤ `i` < `n`. NLopt guarantees that your objective function and any nonlinear constraints will *never* be evaluated outside of these bounds (unlike nonlinear constraints, which may be violated at intermediate steps).
+
+These bounds are specified by passing arrays `lb` and `ub` of length `n` (the dimension of the problem, from `nlopt_create`) to one or both of the functions:
+
+```
+nlopt_result nlopt_set_lower_bounds(nlopt_opt opt, const double* lb);
+nlopt_result nlopt_set_upper_bounds(nlopt_opt opt, const double* ub);
+```
+
+
+(Note that these functions make a copy of the `lb` and `ub` arrays, so subsequent changes to the caller's `lb` and `ub` arrays have no effect on the `opt` object.)
+
+If a lower/upper bound is not set, the default is no bound (unconstrained, i.e. a bound of infinity); it is possible to have lower bounds but not upper bounds or vice versa. Alternatively, the user can call one of the above functions and explicitly pass a lower bound of `-HUGE_VAL` and/or an upper bound of `+HUGE_VAL` for some optimization parameters to make them have no lower/upper bound, respectively. (`HUGE_VAL` is the standard C constant for a floating-point infinity, found in the `math.h` header file.)
+
+It is permitted to set `lb[i]` `==` `ub[i]` in one or more dimensions; this is equivalent to fixing the corresponding `x[i]` parameter, eliminating it from the optimization.
+
+Note, however, that some of the algorithms in NLopt, in particular most of the global-optimization algorithms, do not support unconstrained optimization and will return an error in `nlopt_optimize` if you do not supply finite lower and upper bounds.
+
+For convenience, the following two functions are supplied in order to set the lower/upper bounds for all optimization parameters to a single constant (so that you don’t have to fill an array with a constant value):
+
+```
+nlopt_result nlopt_set_lower_bounds1(nlopt_opt opt, double lb);
+nlopt_result nlopt_set_upper_bounds1(nlopt_opt opt, double ub);
+```
+
+
+The values of the lower and upper bounds can be retrieved by calling:
+
+```
+nlopt_result nlopt_get_lower_bounds(const nlopt_opt opt, double* lb);
+nlopt_result nlopt_get_upper_bounds(const nlopt_opt opt, double* ub);
+```
+
+
+where `lb` and `ub` are arrays of length `n` that, upon successful return, are set to copies of the lower and upper bounds, respectively.
+
+Nonlinear constraints
+---------------------
+
+Several of the algorithms in NLopt (`MMA`, `COBYLA`, and `ORIG_DIRECT`) also support arbitrary nonlinear inequality constraints, and some additionally allow nonlinear equality constraints (`ISRES` and `AUGLAG`). For these algorithms, you can specify as many nonlinear constraints as you wish by calling the following functions multiple times.
+
+In particular, a nonlinear inequality constraint of the form `fc`(*x*) ≤ 0, where the function `fc` is of the same form as the objective function described above, can be specified by calling:
+
+```
+nlopt_result nlopt_add_inequality_constraint(nlopt_opt opt, nlopt_func fc, void* fc_data, double tol);
+```
+
+
+Just as for the objective function, `fc_data` is a pointer to arbitrary user data that will be passed through to the fc function whenever it is called. The parameter `tol` is a tolerance that is used for the purpose of stopping criteria *only*: a point *x* is considered feasible for judging whether to stop the optimization if `fc`(*x*) ≤ `tol`. A tolerance of zero means that NLopt will try not to consider any x to be converged unless `fc` is strictly non-positive; generally, at least a small positive tolerance is advisable to reduce sensitivity to rounding errors.
+
+(The [return value](#Return_Values.md) is negative if there was an error, e.g. an invalid argument or an out-of-memory situation.)
+
+Similarly, a nonlinear equality constraint of the form `h`(*x*) = 0, where the function `h` is of the same form as the objective function described above, can be specified by calling:
+
+```
+nlopt_result nlopt_add_equality_constraint(nlopt_opt opt, nlopt_func h, void* h_data, double tol);
+```
+
+
+Just as for the objective function, `h_data` is a pointer to arbitrary user data that will be passed through to the `h` function whenever it is called. The parameter tol is a tolerance that is used for the purpose of stopping criteria *only*: a point *x* is considered feasible for judging whether to stop the optimization if |`h`(*x*)| ≤ `tol`. For equality constraints, a small positive tolerance is strongly advised in order to allow NLopt to converge even if the equality constraint is slightly nonzero.
+
+(For any algorithm listed as "derivative-free" below, the `grad` argument to `fc` or `h` will always be `NULL` and need never be computed.)
+
+To remove all of the inequality and/or equality constraints from a given problem `opt`, you can call the following functions:
+
+```
+nlopt_result nlopt_remove_inequality_constraints(nlopt_opt opt);
+nlopt_result nlopt_remove_equality_constraints(nlopt_opt opt);
+```
+
+
+### Vector-valued constraints
+
+In some applications with multiple constraints, it is more convenient to define a single function that returns the values (and gradients) of all constraints at once. For example, different constraint functions might share computations in some way. Or, if you have a large number of constraints, you may wish to compute them in parallel. This possibility is supported by the following function, which defines multiple constraints at once, or equivalently a vector-valued constraint function $\mathbf{c}: \mathbb{R}^n \to \mathbb{R}^m$:
+
+```
+nlopt_result nlopt_add_inequality_mconstraint(nlopt_opt opt, unsigned m,
+ nlopt_mfunc c, void* c_data, const double *tol);
+nlopt_result nlopt_add_equality_mconstraint(nlopt_opt opt, unsigned m,
+ nlopt_mfunc c, void* c_data, const double *tol);
+```
+
+
+Here, `m` is the dimensionality of the constraint result and `tol` points to an array of length `m` of the tolerances in each constraint dimension (or `NULL` for zero tolerances). The constraint function must be of the form:
+
+```
+ void c(unsigned m, double *result, unsigned n, const double* x, double* grad, void* f_data);
+```
+
+
+This evaluates the constraint function(s) $\mathbf{c}(\mathbf{x})$ at the point `x`, an array of length `n` (the same as the dimension passed to `nlopt_create`). Upon return, the output value of the constraints should be stored in `result`, an array of length `m` (the same as the dimension passed to `nlopt_add_*_mconstraint`), so that `result[i]` stores *c*<sub>*i*</sub>.
+
+In addition, if `grad` is non-`NULL`, then `grad` points to an array of length `m*n` which should, upon return, be set to the gradients of the constraint functions with respect to `x`. The `n` dimension of `grad` is stored contiguously, so that $\part c_i / \part x_j$ is stored in `grad[i*n` `+` `j]`.
+
+An inequality constraint corresponds to $c_i \le 0$ for $0 \le i < m$, and an equality constraint corresponds to $c_i = 0$, in both cases with tolerance `tol[i]` for purposes of termination criteria.
+
+(You can add multiple vector-valued constraints and/or scalar constraints in the same problem.)
+
+Stopping criteria
+-----------------
+
+Multiple stopping criteria for the optimization are supported (see also the [Introduction](NLopt_Introduction#Termination_conditions.md)), as specified by the functions to modify a given optimization problem `opt`. The optimization halts whenever any one of these criteria is satisfied. In some cases, the precise interpretation of the stopping criterion depends on the optimization algorithm above (although we have tried to make them as consistent as reasonably possible), and some algorithms do not support all of the stopping criteria.
+
+**Note:** you do not need to use *all* of the stopping criteria! In most cases, you only need one or two, and can omit the remainder (all criteria are disabled by default).
+
+For each stopping criteria, there are (at least) two functions: a `set` function to specify the stopping criterion, and a `get` function to retrieve the current value for that criterion.
+
+```
+nlopt_result nlopt_set_stopval(nlopt_opt opt, double stopval);
+double nlopt_get_stopval(const nlopt_opt opt);
+```
+
+
+Stop when an objective value of at least stopval is found: stop minimizing when an objective value ≤ `stopval` is found, or stop maximizing a value ≥ `stopval` is found. (Setting `stopval` to `-HUGE_VAL` for minimizing or `+HUGE_VAL` for maximizing disables this stopping criterion.)
+
+```
+nlopt_result nlopt_set_ftol_rel(nlopt_opt opt, double tol);
+double nlopt_get_ftol_rel(const nlopt_opt opt);
+```
+
+
+Set relative tolerance on function value: stop when an optimization step (or an estimate of the optimum) changes the objective function value by less than `tol` multiplied by the absolute value of the function value. (If there is any chance that your optimum function value is close to zero, you might want to set an absolute tolerance with `nlopt_set_ftol_abs` as well.) Criterion is disabled if `tol` is non-positive.
+
+```
+nlopt_result nlopt_set_ftol_abs(nlopt_opt opt, double tol);
+double nlopt_get_ftol_abs(const nlopt_opt opt);
+```
+
+
+Set absolute tolerance on function value: stop when an optimization step (or an estimate of the optimum) changes the function value by less than `tol`. Criterion is disabled if `tol` is non-positive.
+
+```
+nlopt_result nlopt_set_xtol_rel(nlopt_opt opt, double tol);
+double nlopt_get_xtol_rel(const nlopt_opt opt);
+```
+
+
+Set relative tolerance on optimization parameters: stop when an optimization step (or an estimate of the optimum) changes every parameter by less than `tol` multiplied by the absolute value of the parameter. (If there is any chance that an optimal parameter is close to zero, you might want to set an absolute tolerance with `nlopt_set_xtol_abs` as well.) Criterion is disabled if `tol` is non-positive.
+
+```
+nlopt_result nlopt_set_xtol_abs(nlopt_opt opt, const double* tol);
+nlopt_result nlopt_get_xtol_abs(const nlopt_opt opt, double *tol);
+```
+
+
+Set absolute tolerances on optimization parameters. `tol` is a pointer to an array of length `n` (the dimension from `nlopt_create`) giving the tolerances: stop when an optimization step (or an estimate of the optimum) changes every parameter `x[i]` by less than `tol[i]`. (Note that this function makes a copy of the `tol` array, so subsequent changes to the caller's `tol` have no effect on `opt`.) In `nlopt_get_xtol_abs`, `tol` must be an array of length `n`, which upon successful return contains a copy of the current tolerances.
+
+For convenience, the following function may be used to set the absolute tolerances in all `n` optimization parameters to the same value:
+
+```
+nlopt_result nlopt_set_xtol_abs1(nlopt_opt opt, double tol);
+```
+
+
+Criterion is disabled if `tol` is non-positive.
+
+```
+nlopt_result nlopt_set_maxeval(nlopt_opt opt, int maxeval);
+int nlopt_get_maxeval(nlopt_opt opt);
+```
+
+
+Stop when the number of function evaluations exceeds `maxeval`. (This is not a strict maximum: the number of function evaluations may exceed maxeval slightly, depending upon the algorithm.) Criterion is disabled if `maxeval` is non-positive.
+
+```
+nlopt_result nlopt_set_maxtime(nlopt_opt opt, double maxtime);
+double nlopt_get_maxtime(nlopt_opt opt);
+```
+
+
+Stop when the optimization time (in seconds) exceeds `maxtime`. (This is not a strict maximum: the time may exceed maxtime slightly, depending upon the algorithm and on how slow your function evaluation is.) Criterion is disabled if `maxtime` is non-positive.
+
+### Forced termination
+
+In certain cases, the caller may wish to *force* the optimization to halt, for some reason unknown to NLopt. For example, if the user presses Ctrl-C, or there is an error of some sort in the objective function. (This is used to implement exception handling in the NLopt wrappers for C++ and other languages.) In this case, it is possible to tell NLopt to halt the optimization gracefully, returning the best point found so far, by calling the following function from *within* your objective or constraint functions:
+
+```
+nlopt_result nlopt_force_stop(nlopt_opt opt);
+```
+
+
+This causes `nlopt_optimize` to halt, returning the `NLOPT_FORCED_STOP` error code (below). It has no effect if not called during `nlopt_optimize`.
+
+If you want to provide a bit more information, you can call
+
+```
+nlopt_result nlopt_set_force_stop(nlopt_opt opt, int val)
+```
+
+
+to set a forced-stop integer value `val`, which can be later retrieved by calling:
+
+```
+int nlopt_get_force_stop(nlopt_opt opt)
+```
+
+
+which returns the last force-stop value that was set since the last `nlopt_optimize`. The force-stop value is reset to zero at the beginning of `nlopt_optimize`. Passing `val=0` to `nlopt_set_force_stop` tells NLopt *not* to force a halt.
+
+Performing the optimization
+---------------------------
+
+Once all of the desired optimization parameters have been specified in a given object `opt`, you can perform the optimization by calling:
+
+```
+nlopt_result nlopt_optimize(nlopt_opt opt, double *x, double *opt_f);
+```
+
+
+On input, `x` is an array of length `n` (the dimension of the problem from `nlopt_create`) giving an initial guess for the optimization parameters. On successful return, `x` contains the optimized values of the parameters, and `opt_f` contains the corresponding value of the objective function.
+
+The return value (see below) is positive on success and negative on failure.
+
+Return values
+-------------
+
+Most of the NLopt functions return an enumerated constant of type `nlopt_result`, which takes on one of the following values:
+
+### Successful termination (positive return values)
+
+```
+NLOPT_SUCCESS` `=` `1
+```
+
+Generic success return value.
+
+```
+NLOPT_STOPVAL_REACHED` `=` `2
+```
+
+Optimization stopped because `stopval` (above) was reached.
+
+```
+NLOPT_FTOL_REACHED` `=` `3
+```
+
+Optimization stopped because `ftol_rel` or `ftol_abs` (above) was reached.
+
+```
+NLOPT_XTOL_REACHED` `=` `4
+```
+
+Optimization stopped because `xtol_rel` or `xtol_abs` (above) was reached.
+
+```
+NLOPT_MAXEVAL_REACHED` `=` `5
+```
+
+Optimization stopped because `maxeval` (above) was reached.
+
+```
+NLOPT_MAXTIME_REACHED` `=` `6
+```
+
+Optimization stopped because `maxtime` (above) was reached.
+
+### Error codes (negative return values)
+
+```
+NLOPT_FAILURE` `=` `-1
+```
+
+Generic failure code.
+
+```
+NLOPT_INVALID_ARGS` `=` `-2
+```
+
+Invalid arguments (e.g. lower bounds are bigger than upper bounds, an unknown algorithm was specified, etcetera).
+
+```
+NLOPT_OUT_OF_MEMORY` `=` `-3
+```
+
+Ran out of memory.
+
+```
+NLOPT_ROUNDOFF_LIMITED` `=` `-4
+```
+
+Halted because roundoff errors limited progress. (In this case, the optimization still typically returns a useful result.)
+
+```
+NLOPT_FORCED_STOP` `=` `-5
+```
+
+Halted because of a [forced termination](#Forced_termination.md): the user called `nlopt_force_stop(opt)` on the optimization’s `nlopt_opt` object `opt` from the user’s objective function or constraints.
+
+Local/subsidiary optimization algorithm
+---------------------------------------
+
+Some of the algorithms, especially MLSL and AUGLAG, use a different optimization algorithm as a subroutine, typically for local optimization. You can change the local search algorithm and its tolerances by calling:
+
+```
+nlopt_result nlopt_set_local_optimizer(nlopt_opt opt, const nlopt_opt local_opt);
+```
+
+
+Here, `local_opt` is another `nlopt_opt` object whose parameters are used to determine the local search algorithm, its stopping criteria, and other algorithm parameters. (However, the objective function, bounds, and nonlinear-constraint parameters of `local_opt` are ignored.) The dimension `n` of `local_opt` must match that of `opt`.
+
+This function makes a copy of the `local_opt` object, so you can freely destroy your original `local_opt` afterwards.
+
+Initial step size
+-----------------
+
+For derivative-free local-optimization algorithms, the optimizer must somehow decide on some initial step size to perturb *x* by when it begins the optimization. This step size should be big enough that the value of the objective changes significantly, but not too big if you want to find the local optimum nearest to *x*. By default, NLopt chooses this initial step size heuristically from the bounds, tolerances, and other information, but this may not always be the best choice.
+
+You can modify the initial step size by calling:
+
+```
+nlopt_result nlopt_set_initial_step(nlopt_opt opt, const double* dx);
+```
+
+
+Here, `dx` is an array of length `n` (the dimension of the problem from `nlopt_create`) containing the (nonzero) initial step size for each component of the optimization parameters `x`. If you pass `NULL` for `dx`, then NLopt will use its heuristics to determine the initial step size. For convenience, if you want to set the step sizes in every direction to be the same value, you can instead call:
+
+```
+nlopt_result nlopt_set_initial_step1(nlopt_opt opt, double dx);
+```
+
+
+You can get the initial step size by calling:
+
+```
+nlopt_result nlopt_get_initial_step(const nlopt_opt opt, const double *x, double *dx);
+```
+
+
+Here, `x` is the same as the initial guess that you plan to pass to `nlopt_optimize` – if you have not set the initial step and NLopt is using its heuristics, its heuristic step size may depend on the initial *x*, which is why you must pass it here. Both `x` and `dx` are arrays of length `n` (the dimension of the problem from `nlopt_create`), where `dx` on successful return contains the initial step sizes.
+
+Stochastic population
+---------------------
+
+Several of the stochastic search algorithms (e.g., `CRS`, `MLSL`, and `ISRES`) start by generating some initial "population" of random points *x*. By default, this initial population size is chosen heuristically in some algorithm-specific way, but the initial population can by changed by calling:
+
+```
+nlopt_result nlopt_set_population(nlopt_opt opt, unsigned pop);
+```
+
+
+(A `pop` of zero implies that the heuristic default will be used.)
+
+Pseudorandom numbers
+--------------------
+
+For stochastic optimization algorithms, we use pseudorandom numbers generated by the [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_twister) algorithm, based on code from Makoto Matsumoto. By default, the [seed](https://en.wikipedia.org/wiki/Random_seed) for the random numbers is generated from the system time, so that you will get a different sequence of pseudorandom numbers each time you run your program. If you want to use a "deterministic" sequence of pseudorandom numbers, i.e. the same sequence from run to run, you can set the seed by calling:
+
+```
+void nlopt_srand(unsigned long seed);
+```
+
+
+Some of the algorithms also support using low-discrepancy sequences (LDS), sometimes known as quasi-random numbers. NLopt uses the Sobol LDS, which is implemented for up to 1111 dimensions.
+
+To reset the seed based on the system time, you can call:
+
+```
+void nlopt_srand_time(void);
+```
+
+
+(Normally, you don't need to call this as it is called automatically. However, it might be useful if you want to "re-randomize" the pseudorandom numbers after calling `nlopt_srand` to set a deterministic seed.)
+
+Vector storage for limited-memory quasi-Newton algorithms
+---------------------------------------------------------
+
+Some of the NLopt algorithms are limited-memory "quasi-Newton" algorithms, which "remember" the gradients from a finite number *M* of the previous optimization steps in order to construct an approximate 2nd derivative matrix. The bigger *M* is, the more storage the algorithms require, but on the other hand they *may* converge faster for larger *M*. By default, NLopt chooses a heuristic value of *M*, but this can be changed/retrieved by calling:
+
+```
+nlopt_result nlopt_set_vector_storage(nlopt_opt opt, unsigned M);
+unsigned nlopt_get_vector_storage(const nlopt_opt opt);
+```
+
+
+Passing *M*=0 (the default) tells NLopt to use a heuristic value. By default, NLopt currently sets *M* to 10 or at most 10 [MiB](W:Mebibyte.md) worth of vectors, whichever is larger.
+
+Preconditioning with approximate Hessians
+-----------------------------------------
+
+If you know the Hessian (second-derivative) matrix of your objective function, i.e. the matrix *H* with $H_{ij} = \frac{\partial^2 f}{\partial x_i \partial x_j}$ for an objective *f*, then in principle this could be used to accelerate local optimization. In fact, even a reasonable *approximation* for *H* could be useful if it captures information about the largest eigenvalues of *H* and the corresponding eigenvectors. Such an approximate Hessian is often called a *preconditioner* in the context of iterative solvers, so we adopt that terminology here.
+
+Currently, support for preconditioners in NLopt is somewhat experimental, and is only used in the `NLOPT_LD_CCSAQ` algorithm. You specify a preconditioned objective function by calling one of:
+
+```
+nlopt_result nlopt_set_precond_min_objective(nlopt_opt opt, nlopt_func f, nlopt_precond pre, void *f_data);
+nlopt_result nlopt_set_precond_min_objective(nlopt_opt opt, nlopt_func f, nlopt_precond pre, void *f_data);
+```
+
+
+which are identical to `nlopt_set_min_objective` and `nlopt_set_max_objective`, respectively, except that they additionally specify a preconditioner `pre`, which is a function of the form:
+
+```
+void pre(unsigned n, const double *x, const double *v, double *vpre, void *f_data);
+```
+
+
+This function should take a vector *v* and should compute *vpre = H(x) v* where *H* is an approximate second derivative at *x*. The CCSAQ algorithm **requires** that your matrix *H* be [positive semidefinite](https://en.wikipedia.org/wiki/Positive-definite_matrix#Positive-semidefinite), i.e. that it be real-symmetric with nonnegative eigenvalues.
+
+Version number
+--------------
+
+To determine the version number of NLopt at runtime, you can call:
+
+```
+void nlopt_version(int *major, int *minor, int *bugfix);
+```
+
+
+For example, NLopt version 3.1.4 would return `*major=3`, `*minor=1`, and `*bugfix=4`.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt Tutorial
+---
+
+In this tutorial, we illustrate the usage of NLopt in various languages via one or two trivial examples.
+
+Example nonlinearly constrained problem
+---------------------------------------
+
+
+
+
+ As a first example, we'll look at the following simple nonlinearly constrained minimization problem:
+
+$$\min_{\mathbf{x}\in\mathbb{R}^2} \sqrt{x_2}$$
+
+
+subject to $x_2 \geq 0$, $x_2 \geq (a_1 x_1 + b_1)^3$, and $x_2 \geq (a_2 x_1 + b_2)^3$
+
+for parameters *a*<sub>1</sub>=2, *b*<sub>1</sub>=0, *a*<sub>2</sub>=-1, *b*<sub>2</sub>=1.
+
+The feasible region defined by these constraints is plotted at right: *x*<sub>2</sub> is constrained to lie above the maximum of two cubics, and the optimum point is located at the intersection (1/3, 8/27) where the objective function takes on the value $\sqrt{8/27} \approx 0.5443310539518\ldots$.
+
+(This problem is especially trivial, because by formulating it in terms of the cube root of *x*<sub>2</sub> you can turn it into a linear-programming problem, but we won't do that here.)
+
+In principle, we don't need the bound constraint *x*<sub>2</sub>≥0, since the nonlinear constraints already imply a positive-*x*<sub>2</sub> feasible region. However, NLopt doesn't guarantee that, on the way to finding the optimum, it won't violate the nonlinear constraints at some intermediate steps, while it *does* guarantee that all intermediate steps will satisfy the bound constraints. So, we will explicitly impose *x*<sub>2</sub>≥0 in order to ensure that the √*x*<sub>2</sub> in our objective is real.
+
+**Note:** The objective function here is not differentiable at *x*<sub>2</sub>=0. This doesn't cause problems in the examples below, but may cause problems with some other algorithms if they try to evaluate the gradient at *x*<sub>2</sub>=0 (e.g. I've seen it cause AUGLAG with a gradient-based solver to fail). To prevent this, you might want to use a small nonzero lower bound instead, e.g. *x*<sub>2</sub>≥10<sup>−6</sup>.
+
+Example in C/C++
+----------------
+
+To implement the above example in C or C++, we would first do:
+
+`#include `<math.h>
+`#include `<nlopt.h>
+
+to include the NLopt header file as well as the standard math header file (needed for things like the `sqrt` function and the `HUGE_VAL` constant), then we would define our objective function as:
+
+```
+double myfunc(unsigned n, const double *x, double *grad, void *my_func_data)
+{
+ if (grad) {
+ grad[0] = 0.0;
+ grad[1] = 0.5 / sqrt(x[1]);
+ }
+ return sqrt(x[1]);
+}
+```
+
+
+There are several things to notice here. First, since this is C, our indices are zero-based, so we have `x[0]` and `x[1]` instead of *x*<sub>1</sub> and *x*<sub>2</sub>. The return value of our function is the objective $\sqrt{x_2}$. Also, if the parameter `grad` is not `NULL`, then we set `grad[0]` and `grad[1]` to the partial derivatives of our objective with respect to `x[0]` and `x[1]`. The gradient is only needed for [gradient-based algorithms](NLopt_Introduction#Gradient-based_versus_derivative-free_algorithms.md); if you use a derivative-free optimization algorithm, `grad` will always be `NULL` and you need never compute any derivatives. Finally, we have an extra parameter `my_func_data` that can be used to pass additional data to `myfunc`, but no additional data is needed here so that parameter is unused.
+
+For the constraints, on the other hand, we *will* have additional data. Each constraint is parameterized by two numbers *a* and *b*, so we will declare a data structure to hold this information:
+
+```
+typedef struct {
+ double a, b;
+} my_constraint_data;
+```
+
+
+Then, we implement our constraint function as follows.
+
+```
+double myconstraint(unsigned n, const double *x, double *grad, void *data)
+{
+ my_constraint_data *d = (my_constraint_data *) data;
+ double a = d->a, b = d->b;
+ if (grad) {
+ grad[0] = 3 * a * (a*x[0] + b) * (a*x[0] + b);
+ grad[1] = -1.0;
+ }
+ return ((a*x[0] + b) * (a*x[0] + b) * (a*x[0] + b) - x[1]);
+ }
+```
+
+
+The form of the constraint function is the same as that of the objective function. Here, the `data` parameter will actually be a pointer to `my_constraint_data` (because this is the type that we will pass to `nlopt_minimize_constrained` below), so we use a typecast to get the constraint data. NLopt always expects constraints to be of the form `myconstraint`(**x**) ≤ 0, so we implement the constraint *x*<sub>2</sub> ≥ (*a* *x*<sub>1</sub> + *b*)<sup>3</sup> as the function (*a* *x*<sub>1</sub> + *b*)<sup>3</sup> − *x*<sub>2</sub>. Again, we only compute the gradient if `grad` is non-`NULL`, which will never occur if we use a derivative-free optimization algorithm.
+
+Now, to specify this optimization problem, we create an "object" of type `nlopt_opt` (an opaque pointer type) and set its various parameters:
+
+```
+double lb[2] = { -HUGE_VAL, 0 }; /* lower bounds */
+nlopt_opt opt;
+```
+
+
+```
+opt = nlopt_create(NLOPT_LD_MMA, 2); /* algorithm and dimensionality */
+nlopt_set_lower_bounds(opt, lb);
+nlopt_set_min_objective(opt, myfunc, NULL);
+```
+
+
+Note that we do not need to set an upper bound (`nlopt_set_upper_bounds`), since we are happy with the default upper bounds (+∞). To add the two inequality constraints, we do:
+
+```
+my_constraint_data data[2] = { {2,0}, {-1,1} };
+```
+
+
+```
+nlopt_add_inequality_constraint(opt, myconstraint, &data[0], 1e-8);
+nlopt_add_inequality_constraint(opt, myconstraint, &data[1], 1e-8);
+```
+
+
+Here, the `1e-8` is an optional tolerance for the constraint: for purposes of convergence testing, a point will be considered feasible if the constraint is violated (is positive) by that tolerance (10<sup>−8</sup>). A nonzero tolerance is a good idea for many algorithms lest tiny errors prevent convergence. Speaking of convergence tests, we should also set one or more stopping criteria, e.g. a relative tolerance on the optimization parameters **x**:
+
+```
+nlopt_set_xtol_rel(opt, 1e-4);
+```
+
+
+There are many more possible parameters that you can set to control the optimization, which are described in detail by the [reference manual](NLopt_Reference.md), but these are enough for our example here (any unspecified parameters are set to innocuous defaults). At this point, we can call nlopt_optimize to actually perform the optimization, starting with some initial guess:
+
+```
+double x[2] = { 1.234, 5.678 }; /* `*`some` `initial` `guess`*` */
+double minf; /* `*`the` `minimum` `objective` `value,` `upon` `return`*` */
+if (nlopt_optimize(opt, x, &minf) < 0) {
+ printf("nlopt failed!\n");
+}
+else {
+ printf("found minimum at f(%g,%g) = %0.10g\n", x[0], x[1], minf);
+}
+```
+
+
+`nlopt_optimize` will return a negative result code on failure, but this usually only happens if you pass invalid parameters, it runs out of memory, or something like that. (Actually, most of the other NLopt functions also return an error code that you can check if you are paranoid.) (However, if it returns the failure code `NLOPT_ROUNDOFF_LIMITED`, indicating a breakdown due to roundoff errors, the minimum found may still be useful and you may want to still use it.) Otherwise, we print out the minimum function value and the corresponding parameters **x**.
+
+Finally, we should call nlopt_destroy to dispose of the `nlopt_opt` object when we are done with it:
+
+```
+nlopt_destroy(opt);
+```
+
+
+Assuming we save this in a file tutorial.c, we would compile and link (on Unix) with:
+
+```
+cc tutorial.c -o tutorial -lnlopt -lm
+```
+
+
+The result of running the program should then be something like:
+
+```
+found minimum at f(0.333334,0.296296) = 0.544330847
+```
+
+
+That is, it found the correct parameters to about 5 significant digits and the correct minimum function value to about 6 significant digits. (This is better than we specified; this often occurs because the local optimization routines usually try to be conservative in estimating the error.)
+
+### Number of evaluations
+
+Let's modify our program to print out the number of function evaluations that were required to obtain this result. First, we'll change our objective function to:
+
+```
+int count = 0;
+double myfunc(int n, const double *x, double *grad, void *my_func_data)
+{
+ ++count;
+ if (grad) {
+ grad[0] = 0.0;
+ grad[1] = 0.5 / sqrt(x[1]);
+ }
+ return sqrt(x[1]);
+}
+```
+
+
+using a global variable `count` that is incremented for each function evaluation. (We could also pass a pointer to a counter variable as `my_func_data`, if we wanted to avoid global variables.) Then, adding a `printf`:
+
+```
+printf("found minimum after %d evaluations\n", count);
+```
+
+
+we obtain:
+
+```
+found minimum after 11 evaluations
+found minimum at f(0.333334,0.296296) = 0.544330847
+```
+
+
+For such a simple problem, a gradient-based local optimization algorithm like MMA can converge very quickly!
+
+### Switching to a derivative-free algorithm
+
+We can also try a derivative-free algorithm. Looking at the [NLopt Algorithms](NLopt_Algorithms.md) list, another algorithm in NLopt that handles nonlinear constraints is COBYLA, which is derivative-free. To use it, we just change `NLOPT_LD_MMA` ("LD" means local optimization, derivative/gradient-based) into `NLOPT_LN_COBYLA` ("LN" means local optimization, no derivatives), and obtain:
+
+```
+found minimum after 31 evaluations
+found minimum at f(0.333329,0.2962) = 0.544242301
+```
+
+
+In such a low-dimensional problem, derivative-free algorithms usually work quite well—in this case, it only triples the number of function evaluations. However, the comparison is not perfect because, for the same relative **x** tolerance of 10<sup>−4</sup>, COBYLA is a bit less conservative and only finds the solution to 3 significant digits.
+
+To do a fairer comparison of the two algorithms, we could set the **x** tolerance to zero and ask how many function evaluations each one requires to get the correct answer to three decimal places. We can specify this by using the `stopval` termination criterion, which allows us to halt the process as soon as a feasible point attains an objective function value less than `stopval`. In this case, we would set `stopval` to $\sqrt(8/27)+10^{-3}$, replacing `nlopt_set_xtol_rel` with the statement:
+
+```
+nlopt_set_stopval(opt, sqrt(8./27.)+1e-3);
+```
+
+
+corresponding to the last line of arguments to `nlopt_minimize_constrained` being `sqrt(8./27.)+1e-3,` `0.0,` `0.0,` `0.0,` `NULL,` `0,` `0.0`. If we do this, we find that COBYLA requires 25 evaluations while MMA requires 10.
+
+The advantage of gradient-based algorithms over derivative-free algorithms typically grows for higher-dimensional problems. On the other hand, derivative-free algorithms are much easier to use because you don't need to worry about how to compute the gradient (which might be tricky if the function is very complicated).
+
+Example in C++
+--------------
+
+Although it is perfectly possible to use the C interface from C++, many C++ programmers will find it more natural to use real C++ objects instead of opaque `nlopt_opt` pointers, `std::vector`<double> instead of arrays, and exceptions instead of error codes. NLopt provides a C++ header file `nlopt.hpp` that you can use for this purpose, which simply wraps a C++ object interface around the C interface above.
+
+`#include `<nlopt.hpp>
+
+The equivalent of the above example would then be:
+
+```
+nlopt::opt opt(nlopt::LD_MMA, 2);
+std::vector`<double>` lb(2);
+lb[0] = -HUGE_VAL; lb[1] = 0;
+opt.set_lower_bounds(lb);
+opt.set_min_objective(myfunc, NULL);
+my_constraint_data data[2] = { {2,0}, {-1,1} };
+opt.add_inequality_constraint(myconstraint, &data[0], 1e-8);
+opt.add_inequality_constraint(myconstraint, &data[1], 1e-8);
+opt.set_xtol_rel(1e-4);
+std::vector`<double>` x(2);
+x[0] = 1.234; x[1] = 5.678;
+double minf;
+nlopt::result result = opt.optimize(x, minf);
+```
+
+
+There is no need to deallocate the `opt` object; its destructor will do that for you once it goes out of scope. Also, there is no longer any need to check for error codes; the NLopt C++ functions will throw exceptions if there is an error, which you can `catch` normally.
+
+Here, we are using the same objective and constraint functions as in C, taking `double*` array arguments. Alternatively, you can define objective and constraint functions to take `std::vector`<double> arguments if you prefer. (Using `std::vector`<double> in the objective/constraint imposes a slight overhead because NLopt must copy the `double*` data to a `std::vector`<double>, but this overhead is unlikely to be significant in most real applications.) That is, you would do:
+
+```
+double myvfunc(const std::vector`<double>` &x, std::vector`<double>` &grad, void *my_func_data)
+{
+ if (!grad.empty()) {
+ grad[0] = 0.0;
+ grad[1] = 0.5 / sqrt(x[1]);
+ }
+ return sqrt(x[1]);
+}
+```
+
+
+```
+double myvconstraint(const std::vector`<double>` &x, std::vector`<double>` &grad, void *data)
+{
+ my_constraint_data *d = reinterpret_cast`<my_constraint_data*>`(data);
+ double a = d->a, b = d->b;
+ if (!grad.empty()) {
+ grad[0] = 3 * a * (a*x[0] + b) * (a*x[0] + b);
+ grad[1] = -1.0;
+ }
+ return ((a*x[0] + b) * (a*x[0] + b) * (a*x[0] + b) - x[1]);
+}
+```
+
+
+Notice that, instead of checking whether `grad` is `NULL`, we check whether it is empty. (The vector arguments, if non-empty, are guaranteed to be of the same size as the dimension of the problem that you specified.) We then specify these in the same way as before:
+
+```
+opt.set_min_objective(myvfunc, NULL);
+opt.add_inequality_constraint(myvconstraint, &data[0], 1e-8);
+opt.add_inequality_constraint(myvconstraint, &data[1], 1e-8);
+```
+
+
+Note that the data pointers passed to these functions must remain valid (or rather, what they point to must remain valid) until you are done with `opt`. (It might have been nicer to use `shared_ptr`, but I don't like to rely on bleeding-edge language features.)
+
+Instead of passing a separate data pointer, some users may wish to define a C++ [function object](https://en.wikipedia.org/wiki/Function_object) class that contains all of the data needed by their function, with an overloaded `operator()` method to implement the function call. You can easily do this with a two-line helper function. If your function class is MyFunction, then you could define a static member function:
+
+```
+static double wrap(const std::vector`<double>` &x, std::vector`<double>` &grad, void *data) {
+ return (*reinterpret_cast`<MyFunction*>`(data))(x, grad); }
+```
+
+
+which you would then use e.g. by `opt.set_min_objective(MyFunction::wrap,` `&some_MyFunction)`. Again, you have to make sure that `some_MyFunction` does not go out of scope before you are done calling `nlopt::opt::optimize`.
+
+To link your program, just link to the C NLopt library (`-lnlopt` `-lm` on Unix).
+
+Example in Matlab or GNU Octave
+-------------------------------
+
+To implement this objective function in Matlab (or GNU Octave), we would write a file myfunc.m that looks like:
+
+```
+function [val, gradient] = myfunc(x)
+ val = sqrt(x(2));
+ if (nargout > 1)
+ gradient = [0, 0.5 / val];
+ end
+```
+
+
+Notice that we check the Matlab builtin variable `nargout` (the number of output arguments) to decide whether to compute the gradient. If we use a derivative-free optimization algorithm below, then `nargout` will always be 1 and the gradient need never be computed.
+
+Our constraint function looks similar, except that it is parameterized by the coefficients *a* and *b*. We can just add these on as extra parameters, in a file `myconstraint.m`:
+
+```
+function [val, gradient] = myconstraint(x,a,b)
+ val = (a*x(1) + b)^3 - x(2);
+ if (nargout > 1)
+ gradient = [3*a*(a*x(1) + b)^2, -1];
+ end
+```
+
+
+The equivalent of the `nlopt_opt` is just a [structure](http://www.mathworks.com/access/helpdesk/help/techdoc/matlab_prog/f2-88951.html), with fields corresponding to any parameters that we want to set. (Any structure fields that we don't include are equivalent to not setting those parameters, and using the defaults instead). You can get more information on the available parameters by typing `help` `nlopt_optimize` in Matlab. The equivalent of the C example above is to define an `opt` structure by:
+
+```
+opt.algorithm = NLOPT_LD_MMA
+opt.lower_bounds = [-inf, 0]
+opt.min_objective = @myfunc
+opt.fc = { (@(x) myconstraint(x,2,0)), (@(x) myconstraint(x,-1,1)) }
+opt.fc_tol = [1e-8, 1e-8];
+opt.xtol_rel = 1e-4
+```
+
+
+We do not need to specify the dimension of the problem; this is implicitly specified by the size of the initial-guess vector passed to `nlopt_optimize` below (and must match the sizes of other vectors like `opt.lower_bounds`). The inequality constraints are specified as a [cell array](http://blogs.mathworks.com/loren/2006/06/21/cell-arrays-and-their-contents/) `opt.fc` of function handles (and the corresponding tolerances are in an array `opt.fc_tol`); notice how we use `@(x)` to define an anonymous/inline function in order to pass additional arguments to `myconstraint`.
+
+Finally, we call `nlopt_optimize`:
+
+```
+[xopt, fmin, retcode] = nlopt_optimize(opt, [1.234 5.678])
+```
+
+
+`nlopt_optimize` returns three things: `xopt`, the optimal parameters found; `fmin`, the corresponding value of the objective function, and a return code `retcode` (positive on success and negative on failure).
+
+The output of the above command is:
+
+```
+xopt =
+ 0.3333 0.2963
+fmin = 0.5443
+retcode = 4
+```
+
+
+(The [return code](NLopt_Reference#Return_values.md) `4` corresponds to `NLOPT_XTOL_REACHED`, which means it converged to the specified *x* tolerance.) To switch to a derivative-free algorithm like COBYLA, we just change `opt.algorithm` parameter:
+
+```
+opt.algorithm = NLOPT_LN_COBYLA
+```
+
+
+### Matlab verbose output
+
+It is often useful to print out some status message to see what is happening, especially if your function evaluation is much slower or if a large number of evaluations are required (e.g. for global optimization). You can, of course, modify your function to print out whatever you want. As a shortcut, however, you can set a verbose option in NLopt's Matlab interface by:
+
+```
+opt.verbose = 1;
+```
+
+
+If we do this, then running the MMA algorithm as above yields:
+
+```
+nlopt_minimize_constrained eval #1: 2.38286
+nlopt_minimize_constrained eval #2: 2.35613
+nlopt_minimize_constrained eval #3: 2.24586
+nlopt_minimize_constrained eval #4: 2.0191
+nlopt_minimize_constrained eval #5: 1.74093
+nlopt_minimize_constrained eval #6: 1.40421
+nlopt_minimize_constrained eval #7: 1.0223
+nlopt_minimize_constrained eval #8: 0.685203
+nlopt_minimize_constrained eval #9: 0.552985
+nlopt_minimize_constrained eval #10: 0.544354
+nlopt_minimize_constrained eval #11: 0.544331
+```
+
+
+This shows the objective function values at each intermediate step of the optimization. As in the C example above, it converges in 11 steps. The COBYLA algorithm requires a few more iterations, because it doesn't exploit the gradient information:
+
+```
+nlopt_optimize eval #1: 2.38286
+nlopt_optimize eval #2: 2.38286
+nlopt_optimize eval #3: 3.15222
+nlopt_optimize eval #4: 1.20627
+nlopt_optimize eval #5: 0.499441
+nlopt_optimize eval #6: 0.709216
+nlopt_optimize eval #7: 0.20341
+nlopt_optimize eval #8: 0.745201
+nlopt_optimize eval #9: 0.989693
+nlopt_optimize eval #10: 0.324679
+nlopt_optimize eval #11: 0.804318
+nlopt_optimize eval #12: 0.541431
+nlopt_optimize eval #13: 0.561137
+nlopt_optimize eval #14: 0.531346
+nlopt_optimize eval #15: 0.515784
+nlopt_optimize eval #16: 0.541724
+nlopt_optimize eval #17: 0.541422
+nlopt_optimize eval #18: 0.541504
+nlopt_optimize eval #19: 0.541499
+nlopt_optimize eval #20: 0.541514
+nlopt_optimize eval #21: 0.541352
+nlopt_optimize eval #22: 0.542089
+nlopt_optimize eval #23: 0.542575
+nlopt_optimize eval #24: 0.543027
+nlopt_optimize eval #25: 0.544911
+nlopt_optimize eval #26: 0.541793
+nlopt_optimize eval #27: 0.545225
+nlopt_optimize eval #28: 0.544331
+nlopt_optimize eval #29: 0.544256
+nlopt_optimize eval #30: 0.544242
+nlopt_optimize eval #31: 0.544116
+```
+
+
+Notice that some of the objective function values are below the minimum of 0.54433 — these are simply values of the objective function at infeasible points (violating the nonlinear constraints).
+
+Example in Python
+-----------------
+
+The same example in Python is:
+
+```
+import nlopt
+from numpy import *
+def myfunc(x, grad):
+ if grad.size > 0:
+ grad[0] = 0.0
+ grad[1] = 0.5 / sqrt(x[1])
+ return sqrt(x[1])
+def myconstraint(x, grad, a, b):
+ if grad.size > 0:
+ grad[0] = 3 * a * (a*x[0] + b)**2
+ grad[1] = -1.0
+ return (a*x[0] + b)**3 - x[1]
+opt = nlopt.opt(nlopt.LD_MMA, 2)
+opt.set_lower_bounds([-float('inf'), 0])
+opt.set_min_objective(myfunc)
+opt.add_inequality_constraint(lambda x,grad: myconstraint(x,grad,2,0), 1e-8)
+opt.add_inequality_constraint(lambda x,grad: myconstraint(x,grad,-1,1), 1e-8)
+opt.set_xtol_rel(1e-4)
+x = opt.optimize([1.234, 5.678])
+minf = opt.last_optimum_value()
+print "optimum at ", x[0],x[1]
+print "minimum value = ", minf
+print "result code = ", opt.last_optimize_result()
+```
+
+
+Notice that the `optimize` method returns only the location of the optimum (as a NumPy array), and that the value of the optimum and the result code are obtained by `last_optimum_value` and `last_optimize_result` values. Like in C++, the NLopt functions raise exceptions on errors, so we don't need to check return codes to look for errors.
+
+The objective and constraint functions take NumPy arrays as arguments; if the `grad` argument is non-empty it must be modified *in-place* to the value of the gradient. Notice how we use Python's `lambda` construct to pass additional parameters to the constraints. Alternatively, we could define the objective/constraints as classes with a `__call__(self,` `x,` `grad)` method so that they can behave like functions.
+
+The result of running the above code should be:
+
+```
+optimum at 0.333333331366 0.296296292697
+minimum value = 0.544331050646
+result = 4
+```
+
+
+finding the same correct optimum as in the C interface (of course). (The [return code](NLopt_Reference#Return_values.md) `4` corresponds to `nlopt.XTOL_REACHED`, which means it converged to the specified *x* tolerance.)
+
+### Important: Modifying `grad` in-place
+
+The grad argument of your objective/constraint functions must be modified *in-place*. If you use an operation like
+
+```
+grad = 2*x
+```
+
+
+however, Python allocates a new array to hold `2*x` and reassigns grad to point to it, rather than modifying the original contents of grad. **This will not work.** Instead, you should do:
+
+```
+grad[:] = 2*x
+```
+
+
+which *overwrites* the old contents of grad with `2*x`. See also the [NLopt Python Reference](NLopt_Python_Reference#Assigning_results_in-place.md).
+
+Example in GNU Guile (Scheme)
+-----------------------------
+
+In [GNU Guile](https://en.wikipedia.org/wiki/GNU_Guile), which is an implementation of the [Scheme programming language](https://en.wikipedia.org/wiki/Scheme_(programming_language)), the equivalent of the example above would be:
+
+```
+(use-modules (nlopt))
+(define (myfunc x grad)
+ (if grad
+ (begin
+ (vector-set! grad 0 0.0)
+ (vector-set! grad 1 (/ 0.5 (sqrt (vector-ref x 1))))))
+ (sqrt (vector-ref x 1)))
+(define (myconstraint x grad a b)
+ (let ((x0 (vector-ref x 0)) (x1 (vector-ref x 1)))
+ (if grad
+ (begin
+ (vector-set! grad 0 (* 3 a (expt (+ (* a x0) b) 2)))
+ (vector-set! grad 1 -1.0)))
+ (- (expt (+ (* a x0) b) 3) x1)))
+(define opt (new-nlopt-opt NLOPT-LD-MMA 2))
+(nlopt-opt-set-lower-bounds opt (vector (- (inf)) 0))
+(nlopt-opt-set-min-objective opt myfunc)
+(nlopt-opt-add-inequality-constraint opt (lambda (x grad)
+ (myconstraint x grad 2 0))
+ 1e-8)
+(nlopt-opt-add-inequality-constraint opt (lambda (x grad)
+ (myconstraint x grad -1 1))
+ 1e-8)
+(nlopt-opt-set-xtol-rel opt 1e-4)
+(define x (nlopt-opt-optimize opt (vector 1.234 5.678)))
+(define minf (nlopt-opt-last-optimum-value opt))
+(define result (nlopt-opt-last-optimize-result opt))
+```
+
+
+Note that the objective/constraint functions take two arguments, `x` and `grad`, and return a number. `x` is a vector whose length is the dimension of the problem; grad is either false (`#f`) if it is not needed, or a `vector` that must be modified *in-place* to the gradient of the function.
+
+On error conditions, the NLopt functions throw [exceptions](http://www.gnu.org/software/guile/manual/html_node/Exceptions.html) that can be caught by your Scheme code if you wish.
+
+The heavy use of side-effects here is a bit unnatural in Scheme, but is used in order to closely map to the C++ interface. (Notice that `nlopt::` C++ functions map to `nlopt-` Guile functions, and `nlopt::opt::` methods map to `nlopt-opt-` functions that take the `opt` object as the first argument.) Of course, you are free to wrap your own Scheme-like functional interface around this if you wish.
+
+Example in Fortran
+------------------
+
+In [Fortran](https://en.wikipedia.org/wiki/Fortran), the equivalent of the C example above would be as follows. First, we would write our functions as:
+
+```
+ subroutine myfunc(val, n, x, grad, need_gradient, f_data)
+ double precision val, x(n), grad(n)
+ integer n, need_gradient
+ if (need_gradient.ne.0) then
+ grad(1) = 0.0
+ grad(2) = 0.5 / dsqrt(x(2))
+ endif
+ val = dsqrt(x(2))
+ end
+```
+
+
+```
+ subroutine myconstraint(val, n, x, grad, need_gradient, d)
+ integer need_gradient
+ double precision val, x(n), grad(n), d(2), a, b
+ a = d(1)
+ b = d(2)
+ if (need_gradient.ne.0) then
+ grad(1) = 3. * a * (a*x(1) + b)**2
+ grad(2) = -1.0
+ endif
+ val = (a*x(1) + b)**3 - x(2)
+ end
+```
+
+
+Notice that that the "functions" are actually subroutines. This is because it turns out to be hard to call Fortran functions from C or vice versa in any remotely portable way. Therefore:
+
+- In the NLopt Fortran interface, all C functions become subroutines in Fortran, with the return value becoming the first argument.
+
+So, here the first argument `val` is used for the return value. Also, because there is no way in Fortran to pass `NULL` for the `grad` argument, we add an additional `need_gradient` argument which is nonzero if the gradient needs to be computed. Finally, the last argument is the equivalent of the `void*` argument in the C API, and can be used to pass a single argument of any type through to the objective/constraint functions: here, we use it in `myconstraint` to pass an array of two values for the constants *a* and *b*.
+
+Then, to run the optimization, we can use the following Fortran program:
+
+```
+ program main
+ external myfunc, myconstraint
+ double precision lb(2)
+ integer*8 opt
+ double precision d1(2), d2(2)
+ double precision x(2), minf
+ integer ires
+ include 'nlopt.f'
+
+ call nlo_create(opt, NLOPT_LD_MMA, 2)
+ call nlo_get_lower_bounds(ires, opt, lb)
+ lb(2) = 0.0
+ call nlo_set_lower_bounds(ires, opt, lb)
+ call nlo_set_min_objective(ires, opt, myfunc, 0)
+
+ d1(1) = 2.
+ d1(2) = 0.
+ call nlo_add_inequality_constraint(ires, opt,
+ $ myconstraint, d1, 1.D-8)
+ d2(1) = -1.
+ d2(2) = 1.
+ call nlo_add_inequality_constraint(ires, opt,
+ $ myconstraint, d2, 1.D-8)
+
+ call nlo_set_xtol_rel(ires, opt, 1.D-4)
+
+ x(1) = 1.234
+ x(2) = 5.678
+ call nlo_optimize(ires, opt, x, minf)
+ if (ires.lt.0) then
+ write(*,*) 'nlopt failed!'
+ else
+ write(*,*) 'found min at ', x(1), x(2)
+ write(*,*) 'min val = ', minf
+ endif
+
+ call nlo_destroy(opt)
+
+ end
+```
+
+
+There are a few things to note here:
+
+- All `nlopt_` functions are converted into `nlo_` subroutines, with return values converted into the first argument.
+- The "`nlopt_opt`" variable `opt` is declared as `integer*8`. (Technically, we could use any type that is big enough to hold a pointer on all platforms; `integer*8` is big enough for pointers on both 32-bit and 64-bit machines.)
+- The subroutines must be declared as `external`.
+- We `include` `'nlopt.f'` in order to get the various constants like `NLOPT_LD_MMA`.
+
+There is no standard Fortran 77 equivalent of C's `HUGE_VAL` constant, so instead we just call `nlo_get_lower_bounds` to get the default lower bounds (-∞) and then change one of them. In Fortran 90 (and supported as an extension in many Fortran 77 compilers), there is a `huge` intrinsic function that we could have used instead:
+
+```
+ lb(1) = -huge(lb(1))
+```
+
+
+Example in Julia
+----------------
+
+The same example in the [Julia programming language](https://en.wikipedia.org/wiki/Julia_(programming_language)) can be found at the [NLopt.jl](https://github.com/stevengj/NLopt.jl) web page.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt manual
+---
+
+Welcome to the manual for [NLopt](index.md), our nonlinear optimization library. The manual is divided into a the following sections:
+
+- [NLopt Introduction](NLopt_Introduction.md) — overview of the library and the problems that it solves
+- [NLopt Installation](NLopt_Installation.md) — installation instructions
+- [NLopt Tutorial](NLopt_Tutorial.md) — some simple examples in C, Fortran, and Octave/Matlab
+- [NLopt Reference](NLopt_Reference.md) — reference manual, listing the NLopt API functions
+- [NLopt Algorithms](NLopt_Algorithms.md) — the optimization algorithms available in NLopt (including literature citations and links to original source code, where available)
+- [NLopt License and Copyright](NLopt_License_and_Copyright.md) — legal information
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt on Windows
+---
+
+NLopt on Windows
+----------------
+
+NLopt works fine on Microsoft Windows computers. To simplify installation, we provide a precompiled 32-bit and 64-bit Windows [DLLs](https://en.wikipedia.org/wiki/Dynamic-link_library), built with [MinGW](https://en.wikipedia.org/wiki/MinGW):
+
+- [nlopt-2.4.2-dll32.zip](http://ab-initio.mit.edu/nlopt/nlopt-2.4.2-dll32.zip) (32-bit)
+- [nlopt-2.4.2-dll64.zip](http://ab-initio.mit.edu/nlopt/nlopt-2.4.2-dll64.zip) (64-bit)
+
+Be sure to read the `README-WINDOWS` file included in this [zip](https://en.wikipedia.org/wiki/ZIP_(file_format)) archive for how to build an [import library](http://msdn.microsoft.com/en-us/library/0b9xe492.aspx) for the DLL before using, by running the `lib` `/def:libnlopt-0.def` command (which comes with Microsoft compilers). If you are using GNU compilers (MinGW), run `dlltool` `--input-def` `libnlopt-0.def` `--dllname` `libnlopt-0.dll` `--output-lib` `libnlopt-0.lib` (dlltool comes with MinGW).
+
+(For source code, download the [main `.tar.gz` package](NLopt#Download_and_installation.md).)
+
+Alternatively, you can use the following files, provided by Benoit Scherrer (`benoitscherrer` ατ `gmail.com`), to compile NLopt from source on Windows (with the Microsoft compiler) using [CMake](https://en.wikipedia.org/wiki/CMake):
+
+- [CMakeLists.txt](http://ab-initio.mit.edu/nlopt/CMakeLists.txt) and [config.cmake.h.in](http://ab-initio.mit.edu/nlopt/config.cmake.h.in)
+
+Unofficial Python binaries for Windows are available from Christoph Gohike:
+
+- [Python binaries for 64-bit Windows](http://www.lfd.uci.edu/~gohlke/pythonlibs/#nlopt)
+
+### Octave plugin
+
+To build the NLopt plugin for [GNU Octave](https://en.wikipedia.org/wiki/GNU_Octave) (a free Matlab clone, which uses the [same NLopt interface as in Matlab](NLopt_Matlab_Reference.md)), you will need the following additional steps. (See [Octave for Windows](http://wiki.octave.org/wiki.pl?OctaveForWindows) on the Octave web page to download Octave.)
+
+1. First, download *both* the `.zip` file above and the main `.tar.gz` package of NLopt. Use `dlltool` (which comes with Octave in the *octave*`\mingw23\bin` directory) to create the `.lib` import library as explained above.
+2. Unpack the NLopt .tar.gz file, and copy the `nlopt_optimize-oct.cc` from the *nlopt*`\octave` directory, along with downloading [nlopt_optimize_usage.h](http://jdj.mit.edu/~stevenj/nlopt_optimize_usage.h), and put them together with your `.lib` and `.dll` files (from the `.zip`).
+3. Compile the Octave plugin (`.oct` file) with `mkoctfile` `-lnlopt-0` `--output` `nlopt_optimize.oct` `nlopt_optimize-oct.cc` (`mkoctfile` is a program included with Octave).
+4. Finally, move `libnlopt-0.dll` to the *octave*`\bin` directory so that Octave can find it.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt release notes
+---
+
+Here, we describe what has changed between releases of the [NLopt](index.md) package. You can also refer to the `NEWS` file in the Meep package (or the `ChangeLog` file for a more detailed listing).
+
+NLopt 2.4.2
+-----------
+
+<small>20 May 2014</small>
+
+- Fix CRS for empty dimensions (where lower `==` upper bound) ([issue \#13](https://github.com/stevengj/nlopt/issues/13)).
+
+<!-- -->
+
+- Improvements to CMake (thanks to @xantares) and Windows builds ([issue \#12](https://github.com/stevengj/nlopt/issues/12)).
+
+<!-- -->
+
+- Fix guile2 compatibility ([issue \#21](https://github.com/stevengj/nlopt/issues/21)).
+
+NLopt 2.4.1
+-----------
+
+<small>19 November 2013</small>
+
+- Use [cdecl calling convention instead of stdcall](https://en.wikipedia.org/wiki/X86_calling_conventions) on Win32, to simplify shared-library usage and for consistency with Win64.
+
+NLopt 2.4
+---------
+
+<small>2 November 2013</small>
+
+- New genetic algorithm ESCH, thanks to Carlos Henrique da Silva Santos.
+
+<!-- -->
+
+- Fix swig dir for VPATH builds, thanks to Sandro Vitenti for the bug report.
+
+<!-- -->
+
+- Use python-config program in the configure script to find the include directories for Python, if possible (may be overridden by PYTHON_CONFIG environment variable).
+
+<!-- -->
+
+- Bugfix in copy constructor for C++ and Python interfaces.
+
+<!-- -->
+
+- Bugfix in return value for setting min/max objective.
+
+<!-- -->
+
+- Handle negative rescalings in COBYLA and BOBYQA.
+
+<!-- -->
+
+- Plugin installation honors the configure `--prefix`, if any (thanks to xantares@github).
+
+<!-- -->
+
+- Various compilation fixes for compatibility with recent software.
+
+NLopt 2.3
+---------
+
+<small>20 July 2012</small>
+
+- In Matlab/Octave interface, make returning NaN from the objective equivalent to `nlopt_force_stop`; thanks to Norman Violet for the suggestion.
+- Added CCSA-quadratic (`NLOPT_LD_CCSAQ`), similar to MMA.
+- Added interface for supplying a preconditioner (approximate Hessian); currently only supported in CCSAQ.
+- When adding mconstraints, allow `tol==NULL` as synonym for zero tolerances.
+- Added missing `NLOPT_LD_SLSQP` constant in Matlab/Octave.
+- Lower tolerance for dual optimization in MMA/CCSAQ; thanks to Christophe Leruste for the problem report.
+- Fixed bug in timer, thanks to William Vaughn for the patch.
+- Bug fix to convergence test in SBPLX; thanks to Douglas Bates.
+
+NLopt 2.2.4
+-----------
+
+<small>9 June 2011</small>
+
+- Fixed linking problem for C++ and Python shared libraries on MacOS X; thanks to Volker Lorrmann for the bug report.
+
+NLopt 2.2.3
+-----------
+
+<small>8 June 2011</small>
+
+- Fixed additional re-entrancy problem in Luksan algorithms missed in the previous version; thanks to Gert Wollny for the bug report.
+- Fixed set/get `vector_storage` in Fortran interface for Fortran compilers with all-uppercase linkage.
+
+NLopt 2.2.2
+-----------
+
+<small>26 May 2011</small>
+
+- Added `set_vector_storage` API to modify the memory usage and the subspace dimension for low-storage quasi-Newton methods.
+- Fixed missing support for `maxtime` stopping criteria in Luksan and `ORIG_DIRECT` algorithms; thanks to Jurgen Werner for the bug report.
+- Fixed algorithms to support the case where the lower and upper bounds are equal for some variables (which effectively eliminates those variables from optimization).
+- Added missing `xtol` check to SLSQP, which caused erroneous `ROUNDOFF_LIMITED` error codes to be returned; thanks to Alexander Riess for the bug report.
+- Fixed slight overcounting of function evaluations for `maxeval` check in SLSQP.
+- Fixed deprecated API to support `xtol_abs` `==` `NULL` for backward compatibility (thanks to Francesco Biscani for the bug report).
+- Made Luksan algorithms (e.g. LBFGS and other quasi-Newton methods) re-entrant; thanks to Gert Wollny for the bug report. (Fixes [Gentoo bug \#368685](http://bugs.gentoo.org/show_bug.cgi?id=368685).)
+- Fixed bug in DIRECT (not ORIG_DIRECT), where a typo caused suboptimal convergence in some cases; thanks to Sinisa Hristov for the bug report.
+
+NLopt 2.2.1
+-----------
+
+<small>6 September 2010</small>
+
+- If you compile `nlopt.h` with the `NLOPT_DLL_EXPORT` symbol `#define`d, it now uses the `dllexport` directive (under Windows), useful for compiling an NLopt DLL under Microsoft compilers; thanks to Benoit Scherrer for the suggestion.
+- Handle case where `copysign` function is missing, e.g. on Windows; thanks to Benoit Scherrer for the bug report.
+- Remove C99-style mixed declaration and code in a couple files, so that code compiles in C89; thanks to Benoit Scherrer for the bug report.
+- Removed a few compiler warnings under Microsoft compilers; thanks to Benoit Scherrer for the bug report.
+- Export `nlopt_get_algorithm_name` function on Windows; thanks to Ofek Shilon for the bug report.
+- Don't use `dllimport` directive with `lcc` on Windows (which doesn't support it); thanks to Laurent Vanbeylen for the bug report.
+- Update Nodedal `README` file to indicate that Nocedal's LBFGS code is now available under the GPL, and therefore may be distributed with a future NLopt version (although Luksan's LBFGS code already works well).
+- Bug fix in `set`/`get_xtol_abs`; thanks to David Rivest-Henault for the report.
+
+NLopt 2.2
+---------
+
+<small>15 July 2010</small>
+
+- Added SLSQP algorithm for gradient-based local optimization with nonlinear constraints via sequential quadratic programming, based on the implementation by Dieter Kraft that was adapted for SciPy.
+- Modified BOBYQA and COBYLA algorithms to support unequal initial step sizes in different directions; thanks to Tom Fiddaman for pointing out the need for this in the case where different directions have very different scales.
+- Added Python module docstring; thanks to Sebastian Walter for the suggestion.
+- Added `GUILE_INSTALL_DIR` variable to allow the user to change the Guile installation directory.
+- Added Fortran interface for vector-valued constraints.
+- Throw correct exceptions in Python for the `add_*constraint` functions; thanks to Dmitrey Kroshko for the bug report.
+- Support forced stop and exceptions in `ORIG_DIRECT` algorithms.
+- Remove arbitrary 10<sup>20</sup> upper bound on function values from ORIG_DIRECT code.
+- Bugfix in C++ interface (and some other language front-ends) when deallocating the `nlopt_opt` object in cases like MLSL where `local_optimizer` is used; thanks to Jürgen Werner for the bug report.
+
+NLopt 2.1.2
+-----------
+
+<small>8 July 2010</small>
+
+- The Python `mconstraint` (vector-valued constraint) functions now pass a 2-dimensional array for the gradient argument, rather than a flattened 1d array.
+- Improved handling of exceptions and forced stops for constrained optimization, making sure that no constraints are evaluated after the stop.
+- Return an `NLOPT_INVALID_ARGS` error if more than *n* equality constraints are added in an *n*-dimensional problem.
+- Fix bug that could cause spurious `NLOPT_INVALID_ARGS` errors when adding constraints under rare circumstances.
+
+NLopt 2.1.1
+-----------
+
+<small>7 July 2010</small>
+
+- More robust `configure` check for Python include directories, via `distutils.sysconfig.get_python_inc()` and `numpy.get_include()`. Thanks to Nathaniel Smith for the tip.
+- Bug fix in Guile interface: added missing prefix to `nlopt-version-major` etcetera.
+
+NLopt 2.1
+---------
+
+<small>6 July 2010</small>
+
+- New vector-valued constraint feature; thanks to Dmitrey Kroshko of OpenOpt for the suggestion.
+- `COBYLA` now accepts equality constraints.
+- Guard against multiple inclusion in nlopt.hpp; thanks to Saul Thurrowgood for the suggestion.
+
+NLopt 2.0.2
+-----------
+
+<small>17 June 2010</small>
+
+- Fixed compilation failure in Microsoft Visual Studio, due to incorrect usage of `__stdcall` keyword; thanks to Dave Katz for the bug report.
+
+NLopt 2.0.1
+-----------
+
+<small>16 June 2010</small>
+
+- Bug fix in Fortran API (for `nlo_get_` functions returning arrays).
+- Fixed buggy compilation with MinGW.
+
+NLopt 2.0
+---------
+
+<small>15 June 2010</small>
+
+- New C API, that works by creating an `nlopt_opt` "object" and then calling functions to set the optimization parameters -- much more extensible than the old API (which is preserved for backwards compatibility). (Updated Fortran, Matlab, and GNU Octave wrappers as well.)
+- C++ `nlopt.hpp` wrapper around C API, allowing namespaces, object constructors/destructors, `std::vector`<double>, and exceptions to be exploited.
+- New nlopt wrappers callable from Python and GNU Guile, generated with the help of [SWIG](https://en.wikipedia.org/wiki/SWIG).
+- New `man` `nlopt` manual page documenting new API.
+- New `AUGLAG` algorithm(s) implementing an augmented-Lagrangian method proposed by Birgin and Martinez (2008), which supports nonlinear equality and inequality constraints "wrapped around" other local/global optimization methods.
+- Added API for nonlinear equality constraints (currently only supported by `AUGLAG` and `ISRES` algorithms).
+- Support inequality constraints directly in `ORIG_DIRECT` algorithms (no need to return NaN when constraint is violated).
+- Inequality/equality constraints now have optional tolerances that are used as conditions in stopping criteria.
+- Pseudo-randomize simplex steps in `COBYLA` algorithm, improving robustness by avoiding accidentally taking steps that don't improve conditioning (which seems to happen sometimes with active bound constraints). The algorithm remains deterministic (a deterministic seed is used), however.
+- Allow `COBYLA` to increase the trust-region radius if the predicted improvement was approximately right and the simplex is OK, following a suggestion in the [SAS manual for PROC NLP](http://www.uc.edu/sashtml/iml/chap17/sect164.htm) that seems to improve convergence speed.
+- Added `nlopt_force_stop` function to force a (graceful) halt to the optimization, and corresponding `NLOPT_FORCED_STOP` return code.
+- Improved thread-safety in random-number generation: thread-local storage is used for random-number state, on compilers that support it (e.g. gcc, Intel, Microsoft), to make the generation thread-safe. In this case, the random-number seed must be set per-thread.
+- Return an error in global-search algorithms if the domain is not finite.
+- Use stdcall convention on Windows; thanks to Alan Young for the suggestion.
+- Added missing absolute-tolerance criteria in Luksan algorithms; thanks to Greg Nicholas for the bug report.
+- Fixed compilation under C++, and use C++ compiler for everything in `--with-cxx` mode; thanks to Greg Nicholas for the bug report.
+- In MMA, only stop at minf_max/stopval if the point is feasible.
+- Fix Matlab mex file to not include unnecessary `nlopt-util.h` file, simplifying Windows compilation.
+
+NLopt 1.2
+---------
+
+<small>18 November 2009</small>
+
+- Added Powell's BOBYQA algorithm for box-constrained optimization without derivatives, an improvement on NEWUOA.
+- Added ISRES evolutionary algorithm, supporting nonlinearly constrained global optimization.
+- New functions `nlopt_`*`{set/get}`*`_stochastic_population` to provide optional greater control over the random "population" sizes in stochastic algorithms (although it still has a sensible default).
+- Bug fix: remove extraneous text accidentally included in `nlopt.f` Fortran include file.
+- Bug fix: configure script now correctly handles Matlab installation when `MEX_INSTALL_DIR` is specified manually by the user.
+
+NLopt 1.1
+---------
+
+<small>12 November 2009</small>
+
+- `configure` script detects whether `--enable-shared` is required in order to compile Matlab and Octave plugins (as is the case on x86_64), and disables compilation of those plugins if `--enable-shared` is not used.
+- Added `--without-octave` and `--without-matlab` configure options to disable Octave and Matlab plugins, respectively.
+- Modified COBYLA algorithm to have better support for bound constraints.
+- Added new `NLOPT_ROUNDOFF_LIMITED` failure code to indicate cases in which optimization breaks down due to roundoff errors, in which case it is possible that useful results were obtained.
+- Experimental support for nonlinear equality constraints via augmented-Lagrangian method.
+- Support for compiling under Windows (ideally with MinGW) as a DLL, although you have to manually add `#define` `NLOPT_DLL` to `nlopt.h` **after** installing (after compiling NLopt).
+- Added several checks for roundoff-related breakdown to NEWUOA code.
+- When only a relative error tolerance is specified, no longer fails to halt when exact convergence to zero is obtained.
+- Workaround for incompatible `qsort_r` functions in [BSD and GNU libc](http://sourceware.org/ml/libc-alpha/2008-12/msg00003.html) by always using my own version; thanks to Wendy Vandoolaeghe and Philippe Preux for the bug report and explanation.
+- Workaround for gcc 3.4.x conflict with HUGE_VAL definition in Solaris ([gcc bug 19933](http://gcc.gnu.org/bugzilla/show_bug.cgi?id=19933)).
+- Better identification of Matlab-plugin installation directory.
+- Fixed identification of Octave-plugin installation directory for recent Octave versions.
+
+NLopt 1.0.1
+-----------
+
+<small>13 November 2008</small>
+
+- Allow user to override Matlab-plugin installation directory with `MEX_INSTALL_DIR`.
+
+<!-- -->
+
+- Bug fix in my DIRECT code that prevented convergence (DIRECT-L unaffected).
+
+<!-- -->
+
+- MLSL needs a nonzero default ftol_rel and/or xtol_rel to ensure that its local searches terminate; use roughly machine precision as defaults.
+
+NLopt 1.0
+---------
+
+<small>11 November 2008</small>
+
+- Initial public release.
+
+[Category:NLopt](index.md)
--- /dev/null
+---
+# NLopt
+---
+
+
+
+
+NLopt
+-----
+
+**NLopt** is a free/open-source library for **nonlinear optimization**, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms. Its features include:
+
+- Callable from [C](NLopt_Reference.md), [C++](NLopt_C-plus-plus_Reference.md), [Fortran](NLopt_Fortran_Reference.md), [Matlab or GNU Octave](NLopt_Matlab_Reference.md), [Python](NLopt_Python_Reference.md), [GNU Guile](NLopt_Guile_Reference.md), [Julia](https://github.com/stevengj/NLopt.jl), [GNU R](NLopt_R_Reference.md), [Lua](https://github.com/rochus-keller/LuaNLopt), and [OCaml](https://bitbucket.org/mkur/nlopt-ocaml).
+- A common interface for [many different algorithms](NLopt_Algorithms.md)—try a different algorithm just by changing one parameter.
+- Support for large-scale optimization (some algorithms scalable to millions of parameters and thousands of constraints).
+- Both global and local optimization algorithms.
+- Algorithms using function values only (derivative-free) and also algorithms exploiting user-supplied gradients.
+- Algorithms for unconstrained optimization, bound-constrained optimization, and general nonlinear inequality/equality constraints.
+- Free/open-source software under the [GNU LGPL](https://en.wikipedia.org/wiki/GNU_Lesser_General_Public_License) (and looser licenses for some portions of NLopt).
+
+See the [NLopt Introduction](NLopt_Introduction.md) for a further overview of the types of problems it addresses.
+
+Download and installation
+-------------------------
+
+Version 2.4.2 of NLopt is the latest version available from our web site:
+
+- [nlopt-2.4.2.tar.gz](http://ab-initio.mit.edu/nlopt/nlopt-2.4.2.tar.gz)
+
+See the [NLopt release notes](NLopt_release_notes.md) for the release history. NLopt is designed to be installed on any Unix-like system (GNU/Linux is fine) with a C compiler, using the standard
+
+```
+./configure && make && sudo make install
+```
+
+
+procedure. See the [NLopt Installation](NLopt_Installation.md) instructions for more information.
+
+For Microsoft Windows, see [NLopt on Windows](NLopt_on_Windows.md) for more information and precompiled libraries.
+
+For **developers**, the latest development sources can be found at [<https://github.com/stevengj/nlopt>](https://github.com/stevengj/nlopt).
+
+Documentation and Mailing Lists
+-------------------------------
+
+See the [NLopt manual](NLopt_Introduction.md) for information on how to use NLopt and what optimization algorithms it includes.
+
+Please [cite NLopt](Citing_NLopt.md) and the authors of the algorithm(s) you use in any publication that stems from your use of NLopt.
+
+### Mailing Lists
+
+The NLopt mailing lists (and their archives) are another source of information about NLopt.
+
+Subscribe to the (read-only) [nlopt-announce mailing list](http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/nlopt-announce) to receive an email when NLopt is updated in the future. Subscribe to the (unmoderated) [nlopt-discuss mailing list](http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/nlopt-discuss) for discussion of questions and ideas about using NLopt.
+
+As an alternative to the *nlopt-announce* mailing list, an [Atom newsfeed](https://en.wikipedia.org/wiki/Atom_(standard)) for NLopt releases is available from the [Freshmeat.net NLopt page](http://freshmeat.net/projects/nlopt).
+
+Acknowledgements
+----------------
+
+We are grateful to the many authors who have published useful optimization algorithms implemented in NLopt, especially those who have provided free/open-source implementations of their algorithms.
+
+*Please cite* these authors if you use their code or the implementation of their algorithm in NLopt. See the documentation for the appropriate citation for each of the [algorithms in NLopt](NLopt_Algorithms.md) — please see the [Citing NLopt](Citing_NLopt.md) information.
+
+Contact and Feedback
+--------------------
+
+If you have questions or problems regarding NLopt, you are encouraged query the [nlopt-discuss mailing list](http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/nlopt-discuss) (see above). As your first resort, please look at the [nlopt-discuss archives](http://ab-initio.mit.edu/pipermail/nlopt-discuss/).
+
+Alternatively, you may directly contact [Steven G. Johnson](http://math.mit.edu/~stevenj) at <stevenj@alum.mit.edu>.
+
+[—Steven G. Johnson](User:Stevenj.md) 18:13, 1 September 2008 (EDT)
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+ <script src="{{ base_url }}/js/jquery-2.1.1.min.js"></script>
+ <script src="{{ base_url }}/js/modernizr-2.8.3.min.js"></script>
+ <script type="text/javascript" src="{{ base_url }}/js/highlight.pack.js"></script>
+ <script src="{{ base_url }}/js/theme.js"></script>
+
+ {%- block extrahead %} {% endblock %}
+
+ {%- for path in extra_javascript %}
+ <script src="{{ path }}"></script>
+ {%- endfor %}
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+ <script>
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+ ga('create', '{{ google_analytics[0] }}', '{{ google_analytics[1] }}');
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+ <div class="wy-grid-for-nav">
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+ </div>
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+ {%- block footer %}
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+ <ul class="wy-breadcrumbs">
+ <li><a href="{{ homepage_url }}"><span class="SmallCaps">NLopt</span> documentation</a> »</li>
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+ <a href="{{ repo_url }}" class="icon icon-github"> Edit on GitHub</a>
+ {% elif repo_name == 'Bitbucket' %}
+ <a href="{{ repo_url }}" class="icon icon-bitbucket"> Edit on BitBucket</a>
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+ border-left:5px solid transparent;
+ border-right:5px solid transparent;
+ position:absolute;
+ display:block;
+ top:-4px;
+ left:50%;
+ margin-left:-3px}
+.wy-dropdown-arrow.wy-dropdown-arrow-left:before
+ {left:11px}
+.wy-form-stacked select
+ {display:block}
+.wy-form-aligned input,.wy-form-aligned textarea,.wy-form-aligned select,.wy-form-aligned .wy-help-inline,.wy-form-aligned label
+ {display:inline-block;
+ *display:inline;
+ *zoom:1;
+ vertical-align:middle}
+.wy-form-aligned .wy-control-group>label
+ {display:inline-block;
+ vertical-align:middle;
+ width:10em;
+ margin:6px 12px 0 0;
+ float:left}
+.wy-form-aligned .wy-control
+ {float:left}
+.wy-form-aligned .wy-control label
+ {display:block}
+.wy-form-aligned .wy-control select
+ {margin-top:6px}
+fieldset
+ {border:0;
+ margin:0;
+ padding:0}
+legend
+ {display:block;
+ width:100%;
+ border:0;
+ padding:0;
+ white-space:normal;
+ margin-bottom:24px;
+ font-size:150%;
+ *margin-left:-7px}
+label
+ {display:block;
+ margin:0 0 0.3125em 0;
+ color:#999;
+ font-size:90%}
+input,select,textarea
+ {font-size:100%;
+ margin:0;
+ vertical-align:baseline;
+ *vertical-align:middle}
+.wy-control-group
+ {margin-bottom:24px;
+ *zoom:1;
+ max-width:68em;
+ margin-left:auto;
+ margin-right:auto;
+ *zoom:1}
+.wy-control-group:before,.wy-control-group:after
+ {display:table;
+ content:""}
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+ {clear:both}
+.wy-control-group:before,.wy-control-group:after
+ {display:table;
+ content:""}
+.wy-control-group:after
+ {clear:both}
+.wy-control-group.wy-control-group-required>label:after
+ {content:" *";
+ color:#E74C3C}
+.wy-control-group .wy-form-full,.wy-control-group .wy-form-halves,.wy-control-group .wy-form-thirds
+ {padding-bottom:12px}
+.wy-control-group .wy-form-full select,.wy-control-group .wy-form-halves select,.wy-control-group .wy-form-thirds select
+ {width:100%}
+.wy-control-group .wy-form-full input[type="text"],.wy-control-group .wy-form-full input[type="password"],.wy-control-group .wy-form-full input[type="email"],.wy-control-group .wy-form-full input[type="url"],.wy-control-group .wy-form-full input[type="date"],.wy-control-group .wy-form-full input[type="month"],.wy-control-group .wy-form-full input[type="time"],.wy-control-group .wy-form-full input[type="datetime"],.wy-control-group .wy-form-full input[type="datetime-local"],.wy-control-group .wy-form-full input[type="week"],.wy-control-group .wy-form-full input[type="number"],.wy-control-group .wy-form-full input[type="search"],.wy-control-group .wy-form-full input[type="tel"],.wy-control-group .wy-form-full input[type="color"],.wy-control-group .wy-form-halves input[type="text"],.wy-control-group .wy-form-halves input[type="password"],.wy-control-group .wy-form-halves input[type="email"],.wy-control-group .wy-form-halves input[type="url"],.wy-control-group .wy-form-halves input[type="date"],.wy-control-group .wy-form-halves input[type="month"],.wy-control-group .wy-form-halves input[type="time"],.wy-control-group .wy-form-halves input[type="datetime"],.wy-control-group .wy-form-halves input[type="datetime-local"],.wy-control-group .wy-form-halves input[type="week"],.wy-control-group .wy-form-halves input[type="number"],.wy-control-group .wy-form-halves input[type="search"],.wy-control-group .wy-form-halves input[type="tel"],.wy-control-group .wy-form-halves input[type="color"],.wy-control-group .wy-form-thirds input[type="text"],.wy-control-group .wy-form-thirds input[type="password"],.wy-control-group .wy-form-thirds input[type="email"],.wy-control-group .wy-form-thirds input[type="url"],.wy-control-group .wy-form-thirds input[type="date"],.wy-control-group .wy-form-thirds input[type="month"],.wy-control-group .wy-form-thirds input[type="time"],.wy-control-group .wy-form-thirds input[type="datetime"],.wy-control-group .wy-form-thirds input[type="datetime-local"],.wy-control-group .wy-form-thirds input[type="week"],.wy-control-group .wy-form-thirds input[type="number"],.wy-control-group .wy-form-thirds input[type="search"],.wy-control-group .wy-form-thirds input[type="tel"],.wy-control-group .wy-form-thirds input[type="color"]
+ {width:100%}
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+ {float:left;
+ display:block;
+ margin-right:2.35765%;
+ width:100%;
+ margin-right:0}
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+ {margin-right:0}
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+ {float:left;
+ display:block;
+ margin-right:2.35765%;
+ width:48.82117%}
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+ {margin-right:0}
+.wy-control-group .wy-form-halves:nth-of-type(2n)
+ {margin-right:0}
+.wy-control-group .wy-form-halves:nth-of-type(2n+1)
+ {clear:left}
+.wy-control-group .wy-form-thirds
+ {float:left;
+ display:block;
+ margin-right:2.35765%;
+ width:31.76157%}
+.wy-control-group .wy-form-thirds:last-child
+ {margin-right:0}
+.wy-control-group .wy-form-thirds:nth-of-type(3n)
+ {margin-right:0}
+.wy-control-group .wy-form-thirds:nth-of-type(3n+1)
+ {clear:left}
+.wy-control-group.wy-control-group-no-input .wy-control
+ {margin:6px 0 0 0;
+ font-size:90%}
+.wy-control-no-input
+ {display:inline-block;
+ margin:6px 0 0 0;
+ font-size:90%}
+.wy-control-group.fluid-input input[type="text"],.wy-control-group.fluid-input input[type="password"],.wy-control-group.fluid-input input[type="email"],.wy-control-group.fluid-input input[type="url"],.wy-control-group.fluid-input input[type="date"],.wy-control-group.fluid-input input[type="month"],.wy-control-group.fluid-input input[type="time"],.wy-control-group.fluid-input input[type="datetime"],.wy-control-group.fluid-input input[type="datetime-local"],.wy-control-group.fluid-input input[type="week"],.wy-control-group.fluid-input input[type="number"],.wy-control-group.fluid-input input[type="search"],.wy-control-group.fluid-input input[type="tel"],.wy-control-group.fluid-input input[type="color"]
+ {width:100%}
+.wy-form-message-inline
+ {display:inline-block;
+ padding-left:0.3em;
+ color:#666;
+ vertical-align:middle;
+ font-size:90%}
+.wy-form-message
+ {display:block;
+ color:#999;
+ font-size:70%;
+ margin-top:0.3125em;
+ font-style:italic}
+input
+ {line-height:normal}
+input[type="button"],input[type="reset"],input[type="submit"]
+ {-webkit-appearance:button;
+ cursor:pointer;
+ font-family:"Lato","proxima-nova","Helvetica Neue",Arial,sans-serif;
+ *overflow:visible}
+input[type="text"],input[type="password"],input[type="email"],input[type="url"],input[type="date"],input[type="month"],input[type="time"],input[type="datetime"],input[type="datetime-local"],input[type="week"],input[type="number"],input[type="search"],input[type="tel"],input[type="color"]
+ {-webkit-appearance:none;
+ padding:6px;
+ display:inline-block;
+ border:1px solid #ccc;
+ font-size:80%;
+ font-family:"Lato","proxima-nova","Helvetica Neue",Arial,sans-serif;
+ box-shadow:inset 0 1px 3px #ddd;
+ border-radius:0;
+ -webkit-transition:border 0.3s linear;
+ -moz-transition:border 0.3s linear;
+ transition:border 0.3s linear}
+input[type="datetime-local"]
+ {padding:0.34375em 0.625em}
+input[disabled]
+ {cursor:default}
+input[type="checkbox"],input[type="radio"]
+ {-webkit-box-sizing:border-box;
+ -moz-box-sizing:border-box;
+ box-sizing:border-box;
+ padding:0;
+ margin-right:0.3125em;
+ *height:13px;
+ *width:13px}
+input[type="search"]
+ {-webkit-box-sizing:border-box;
+ -moz-box-sizing:border-box;
+ box-sizing:border-box}
+input[type="search"]::-webkit-search-cancel-button,input[type="search"]::-webkit-search-decoration
+ {-webkit-appearance:none}
+input[type="text"]:focus,input[type="password"]:focus,input[type="email"]:focus,input[type="url"]:focus,input[type="date"]:focus,input[type="month"]:focus,input[type="time"]:focus,input[type="datetime"]:focus,input[type="datetime-local"]:focus,input[type="week"]:focus,input[type="number"]:focus,input[type="search"]:focus,input[type="tel"]:focus,input[type="color"]:focus
+ {outline:0;
+ outline:thin dotted \9;
+ border-color:#333}
+input.no-focus:focus
+ {border-color:#ccc !important}
+input[type="file"]:focus,input[type="radio"]:focus,input[type="checkbox"]:focus
+ {outline:thin dotted #333;
+ outline:1px auto #129FEA}
+input[type="text"][disabled],input[type="password"][disabled],input[type="email"][disabled],input[type="url"][disabled],input[type="date"][disabled],input[type="month"][disabled],input[type="time"][disabled],input[type="datetime"][disabled],input[type="datetime-local"][disabled],input[type="week"][disabled],input[type="number"][disabled],input[type="search"][disabled],input[type="tel"][disabled],input[type="color"][disabled]
+ {cursor:not-allowed;
+ background-color:#f3f6f6;
+ color:#cad2d3}
+input:focus:invalid,textarea:focus:invalid,select:focus:invalid
+ {color:#E74C3C;
+ border:1px solid #E74C3C}
+input:focus:invalid:focus,textarea:focus:invalid:focus,select:focus:invalid:focus
+ {border-color:#E74C3C}
+input[type="file"]:focus:invalid:focus,input[type="radio"]:focus:invalid:focus,input[type="checkbox"]:focus:invalid:focus
+ {outline-color:#E74C3C}
+input.wy-input-large
+ {padding:12px;
+ font-size:100%}
+textarea
+ {overflow:auto;
+ vertical-align:top;
+ width:100%;
+ font-family:"Lato","proxima-nova","Helvetica Neue",Arial,sans-serif}
+select,textarea
+ {padding:0.5em 0.625em;
+ display:inline-block;
+ border:1px solid #ccc;
+ font-size:80%;
+ box-shadow:inset 0 1px 3px #ddd;
+ -webkit-transition:border 0.3s linear;
+ -moz-transition:border 0.3s linear;
+ transition:border 0.3s linear}
+select
+ {border:1px solid #ccc;
+ background-color:#fff}
+select[multiple]
+ {height:auto}
+select:focus,textarea:focus
+ {outline:0}
+select[disabled],textarea[disabled],input[readonly],select[readonly],textarea[readonly]
+ {cursor:not-allowed;
+ background-color:#fff;
+ color:#cad2d3;
+ border-color:transparent}
+.wy-checkbox,.wy-radio
+ {margin:6px 0;
+ color:#404040;
+ display:block}
+.wy-checkbox input,.wy-radio input
+ {vertical-align:baseline}
+.wy-form-message-inline
+ {display:inline-block;
+ *display:inline;
+ *zoom:1;
+ vertical-align:middle}
+.wy-input-prefix,.wy-input-suffix
+ {white-space:nowrap}
+.wy-input-prefix .wy-input-context,.wy-input-suffix .wy-input-context
+ {padding:6px;
+ display:inline-block;
+ font-size:80%;
+ background-color:#f3f6f6;
+ border:solid 1px #ccc;
+ color:#999}
+.wy-input-suffix .wy-input-context
+ {border-left:0}
+.wy-input-prefix .wy-input-context
+ {border-right:0}
+.wy-control-group.wy-control-group-error .wy-form-message,.wy-control-group.wy-control-group-error>label
+ {color:#E74C3C}
+.wy-control-group.wy-control-group-error input[type="text"],.wy-control-group.wy-control-group-error input[type="password"],.wy-control-group.wy-control-group-error input[type="email"],.wy-control-group.wy-control-group-error input[type="url"],.wy-control-group.wy-control-group-error input[type="date"],.wy-control-group.wy-control-group-error input[type="month"],.wy-control-group.wy-control-group-error input[type="time"],.wy-control-group.wy-control-group-error input[type="datetime"],.wy-control-group.wy-control-group-error input[type="datetime-local"],.wy-control-group.wy-control-group-error input[type="week"],.wy-control-group.wy-control-group-error input[type="number"],.wy-control-group.wy-control-group-error input[type="search"],.wy-control-group.wy-control-group-error input[type="tel"],.wy-control-group.wy-control-group-error input[type="color"]
+ {border:solid 1px #E74C3C}
+.wy-control-group.wy-control-group-error textarea
+ {border:solid 1px #E74C3C}
+.wy-inline-validate
+ {white-space:nowrap}
+.wy-inline-validate .wy-input-context
+ {padding:0.5em 0.625em;
+ display:inline-block;
+ font-size:80%}
+.wy-inline-validate.wy-inline-validate-success .wy-input-context
+ {color:#27AE60}
+.wy-inline-validate.wy-inline-validate-danger .wy-input-context
+ {color:#E74C3C}
+.wy-inline-validate.wy-inline-validate-warning .wy-input-context
+ {color:#E67E22}
+.wy-inline-validate.wy-inline-validate-info .wy-input-context
+ {color:#2980B9}
+.rotate-90
+ {-webkit-transform:rotate(90deg);
+ -moz-transform:rotate(90deg);
+ -ms-transform:rotate(90deg);
+ -o-transform:rotate(90deg);
+ transform:rotate(90deg)}
+.rotate-180
+ {-webkit-transform:rotate(180deg);
+ -moz-transform:rotate(180deg);
+ -ms-transform:rotate(180deg);
+ -o-transform:rotate(180deg);
+ transform:rotate(180deg)}
+.rotate-270
+ {-webkit-transform:rotate(270deg);
+ -moz-transform:rotate(270deg);
+ -ms-transform:rotate(270deg);
+ -o-transform:rotate(270deg);
+ transform:rotate(270deg)}
+.mirror
+ {-webkit-transform:scaleX(-1);
+ -moz-transform:scaleX(-1);
+ -ms-transform:scaleX(-1);
+ -o-transform:scaleX(-1);
+ transform:scaleX(-1)}
+.mirror.rotate-90
+ {-webkit-transform:scaleX(-1) rotate(90deg);
+ -moz-transform:scaleX(-1) rotate(90deg);
+ -ms-transform:scaleX(-1) rotate(90deg);
+ -o-transform:scaleX(-1) rotate(90deg);
+ transform:scaleX(-1) rotate(90deg)}
+.mirror.rotate-180
+ {-webkit-transform:scaleX(-1) rotate(180deg);
+ -moz-transform:scaleX(-1) rotate(180deg);
+ -ms-transform:scaleX(-1) rotate(180deg);
+ -o-transform:scaleX(-1) rotate(180deg);
+ transform:scaleX(-1) rotate(180deg)}
+.mirror.rotate-270
+ {-webkit-transform:scaleX(-1) rotate(270deg);
+ -moz-transform:scaleX(-1) rotate(270deg);
+ -ms-transform:scaleX(-1) rotate(270deg);
+ -o-transform:scaleX(-1) rotate(270deg);
+ transform:scaleX(-1) rotate(270deg)}
+@media only screen and (max-width: 480px)
+ {.wy-form button[type="submit"]
+ {margin:0.7em 0 0}
+.wy-form input[type="text"],.wy-form input[type="password"],.wy-form input[type="email"],.wy-form input[type="url"],.wy-form input[type="date"],.wy-form input[type="month"],.wy-form input[type="time"],.wy-form input[type="datetime"],.wy-form input[type="datetime-local"],.wy-form input[type="week"],.wy-form input[type="number"],.wy-form input[type="search"],.wy-form input[type="tel"],.wy-form input[type="color"]
+ {margin-bottom:0.3em;
+ display:block}
+.wy-form label
+ {margin-bottom:0.3em;
+ display:block}
+.wy-form input[type="password"],.wy-form input[type="email"],.wy-form input[type="url"],.wy-form input[type="date"],.wy-form input[type="month"],.wy-form input[type="time"],.wy-form input[type="datetime"],.wy-form input[type="datetime-local"],.wy-form input[type="week"],.wy-form input[type="number"],.wy-form input[type="search"],.wy-form input[type="tel"],.wy-form input[type="color"]
+ {margin-bottom:0}
+.wy-form-aligned .wy-control-group label
+ {margin-bottom:0.3em;
+ text-align:left;
+ display:block;
+ width:100%}
+.wy-form-aligned .wy-control
+ {margin:1.5em 0 0 0}
+.wy-form .wy-help-inline,.wy-form-message-inline,.wy-form-message
+ {display:block;
+ font-size:80%;
+ padding:6px 0}
+}
+@media screen and (max-width: 768px)
+ {.tablet-hide
+ {display:none}
+}
+@media screen and (max-width: 480px)
+ {.mobile-hide
+ {display:none}
+}
+.float-left
+ {float:left}
+.float-right
+ {float:right}
+.full-width
+ {width:100%}
+.wy-table,.rst-content table.docutils,.rst-content table.field-list
+ {border-collapse:collapse;
+ border-spacing:0;
+ empty-cells:show;
+ margin-bottom:24px}
+.wy-table caption,.rst-content table.docutils caption,.rst-content table.field-list caption
+ {color:#000;
+ font:italic 85%/1 arial,sans-serif;
+ padding:1em 0;
+ text-align:center}
+.wy-table td,.rst-content table.docutils td,.rst-content table.field-list td,.wy-table th,.rst-content table.docutils th,.rst-content table.field-list th
+ {font-size:90%;
+ margin:0;
+ overflow:visible;
+ padding:8px 16px}
+.wy-table td:first-child,.rst-content table.docutils td:first-child,.rst-content table.field-list td:first-child,.wy-table th:first-child,.rst-content table.docutils th:first-child,.rst-content table.field-list th:first-child
+ {border-left-width:0}
+.wy-table thead,.rst-content table.docutils thead,.rst-content table.field-list thead
+ {color:#000;
+ text-align:left;
+ vertical-align:bottom;
+ white-space:nowrap}
+.wy-table thead th,.rst-content table.docutils thead th,.rst-content table.field-list thead th
+ {font-weight:bold;
+ border-bottom:solid 2px #e1e4e5}
+.wy-table td,.rst-content table.docutils td,.rst-content table.field-list td
+ {background-color:transparent;
+ vertical-align:middle}
+.wy-table td p,.rst-content table.docutils td p,.rst-content table.field-list td p
+ {line-height:18px}
+.wy-table td p:last-child,.rst-content table.docutils td p:last-child,.rst-content table.field-list td p:last-child
+ {margin-bottom:0}
+.wy-table .wy-table-cell-min,.rst-content table.docutils .wy-table-cell-min,.rst-content table.field-list .wy-table-cell-min
+ {width:1%;
+ padding-right:0}
+.wy-table .wy-table-cell-min input[type=checkbox],.rst-content table.docutils .wy-table-cell-min input[type=checkbox],.rst-content table.field-list .wy-table-cell-min input[type=checkbox],.wy-table .wy-table-cell-min input[type=checkbox],.rst-content table.docutils .wy-table-cell-min input[type=checkbox],.rst-content table.field-list .wy-table-cell-min input[type=checkbox]
+ {margin:0}
+.wy-table-secondary
+ {color:gray;
+ font-size:90%}
+.wy-table-tertiary
+ {color:gray;
+ font-size:80%}
+.wy-table-odd td,.wy-table-striped tr:nth-child(2n-1) td,.rst-content table.docutils:not(.field-list) tr:nth-child(2n-1) td
+ {background-color:#f3f6f6}
+.wy-table-backed
+ {background-color:#f3f6f6}
+.wy-table-bordered-all,.rst-content table.docutils
+ {border:1px solid #e1e4e5}
+.wy-table-bordered-all td,.rst-content table.docutils td
+ {border-bottom:1px solid #e1e4e5;
+ border-left:1px solid #e1e4e5}
+.wy-table-bordered-all tbody>tr:last-child td,.rst-content table.docutils tbody>tr:last-child td
+ {border-bottom-width:0}
+.wy-table-bordered
+ {border:1px solid #e1e4e5}
+.wy-table-bordered-rows td
+ {border-bottom:1px solid #e1e4e5}
+.wy-table-bordered-rows tbody>tr:last-child td
+ {border-bottom-width:0}
+.wy-table-horizontal tbody>tr:last-child td
+ {border-bottom-width:0}
+.wy-table-horizontal td,.wy-table-horizontal th
+ {border-width:0 0 1px 0;
+ border-bottom:1px solid #e1e4e5}
+.wy-table-horizontal tbody>tr:last-child td
+ {border-bottom-width:0}
+.wy-table-responsive
+ {margin-bottom:24px;
+ max-width:100%;
+ overflow:auto}
+.wy-table-responsive table
+ {margin-bottom:0 !important}
+.wy-table-responsive table td,.wy-table-responsive table th
+ {white-space:nowrap}
+a
+ {color:#2980B9;
+ text-decoration:none}
+a:hover
+ {color:#3091d1}
+a:visited
+ {color:#9B59B6}
+html
+ {height:100%;
+ overflow-x:hidden}
+body
+ {font-family:"Lato","proxima-nova","Helvetica Neue",Arial,sans-serif;
+ font-weight:normal;
+ color:#404040;
+ min-height:100%;
+ overflow-x:hidden;
+ background:#edf0f2}
+.wy-text-left
+ {text-align:left}
+.wy-text-center
+ {text-align:center}
+.wy-text-right
+ {text-align:right}
+.wy-text-large
+ {font-size:120%}
+.wy-text-normal
+ {font-size:100%}
+.wy-text-small,small
+ {font-size:80%}
+.wy-text-strike
+ {text-decoration:line-through}
+.wy-text-warning
+ {color:#E67E22 !important}
+a.wy-text-warning:hover
+ {color:#eb9950 !important}
+.wy-text-info
+ {color:#2980B9 !important}
+a.wy-text-info:hover
+ {color:#409ad5 !important}
+.wy-text-success
+ {color:#27AE60 !important}
+a.wy-text-success:hover
+ {color:#36d278 !important}
+.wy-text-danger
+ {color:#E74C3C !important}
+a.wy-text-danger:hover
+ {color:#ed7669 !important}
+.wy-text-neutral
+ {color:#404040 !important}
+a.wy-text-neutral:hover
+ {color:#595959 !important}
+h1,h2,h3,h4,h5,h6,legend
+ {margin-top:0;
+ font-weight:700;
+ font-family:"Roboto Slab","ff-tisa-web-pro","Georgia",Arial,sans-serif}
+p
+ {line-height:24px;
+ margin:0;
+ font-size:16px;
+ margin-bottom:24px}
+h1
+ {font-size:175%}
+h2
+ {font-size:150%}
+h3
+ {font-size:125%}
+h4
+ {font-size:115%}
+h5
+ {font-size:110%}
+h6
+ {font-size:100%}
+hr
+ {display:block;
+ height:1px;
+ border:0;
+ border-top:1px solid #e1e4e5;
+ margin:24px 0;
+ padding:0}
+code,.rst-content tt
+ {white-space:nowrap;
+ max-width:100%;
+ background:#fff;
+ border:solid 1px #e1e4e5;
+ font-size:75%;
+ padding:0 5px;
+ font-family:Consolas,"Andale Mono WT","Andale Mono","Lucida Console","Lucida Sans Typewriter","DejaVu Sans Mono","Bitstream Vera Sans Mono","Liberation Mono","Nimbus Mono L",Monaco,"Courier New",Courier,monospace;
+ color:#E74C3C;
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\ No newline at end of file
--- /dev/null
+<footer>
+ {% if next_page or previous_page %}
+ <div class="rst-footer-buttons" role="navigation" aria-label="footer navigation">
+ {% if next_page %}
+ <a href="{{ next_page.url }}" class="btn btn-neutral float-right" title="{{ next_page.title }}"/>Next <span class="icon icon-circle-arrow-right"></span></a>
+ {% endif %}
+ {% if previous_page %}
+ <a href="{{ previous_page.url }}" class="btn btn-neutral" title="{{ previous_page.title }}"><span class="icon icon-circle-arrow-left"></span> Previous</a>
+ {% endif %}
+ </div>
+ {% endif %}
+
+ <hr/>
+
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FourierDCT FourierDCTFilter FourierDCTMatrix FourierDST FourierDSTMatrix FourierMatrix FourierParameters FourierSequenceTransform FourierSeries FourierSinCoefficient FourierSinSeries FourierSinTransform FourierTransform FourierTrigSeries FractionalBrownianMotionProcess FractionalPart FractionBox FractionBoxOptions FractionLine Frame FrameBox FrameBoxOptions Framed FrameInset FrameLabel Frameless FrameMargins FrameStyle FrameTicks FrameTicksStyle FRatioDistribution FrechetDistribution FreeQ FrequencySamplingFilterKernel FresnelC FresnelS Friday FrobeniusNumber FrobeniusSolve FromCharacterCode FromCoefficientRules FromContinuedFraction FromDate FromDigits FromDMS Front FrontEndDynamicExpression FrontEndEventActions FrontEndExecute FrontEndObject FrontEndResource FrontEndResourceString FrontEndStackSize FrontEndToken FrontEndTokenExecute FrontEndValueCache FrontEndVersion FrontFaceColor FrontFaceOpacity Full FullAxes FullDefinition FullForm FullGraphics FullOptions FullSimplify Function FunctionExpand FunctionInterpolation FunctionSpace FussellVeselyImportance GaborFilter GaborMatrix GaborWavelet GainMargins GainPhaseMargins Gamma GammaDistribution GammaRegularized GapPenalty Gather GatherBy GaugeFaceElementFunction GaugeFaceStyle GaugeFrameElementFunction GaugeFrameSize GaugeFrameStyle GaugeLabels GaugeMarkers GaugeStyle GaussianFilter GaussianIntegers GaussianMatrix GaussianWindow GCD GegenbauerC General GeneralizedLinearModelFit GenerateConditions GeneratedCell GeneratedParameters GeneratingFunction Generic GenericCylindricalDecomposition GenomeData GenomeLookup GeodesicClosing GeodesicDilation GeodesicErosion GeodesicOpening GeoDestination GeodesyData GeoDirection GeoDistance GeoGridPosition GeometricBrownianMotionProcess GeometricDistribution GeometricMean GeometricMeanFilter GeometricTransformation GeometricTransformation3DBox GeometricTransformation3DBoxOptions GeometricTransformationBox GeometricTransformationBoxOptions GeoPosition GeoPositionENU GeoPositionXYZ GeoProjectionData GestureHandler GestureHandlerTag Get GetBoundingBoxSizePacket GetContext GetEnvironment GetFileName GetFrontEndOptionsDataPacket GetLinebreakInformationPacket GetMenusPacket GetPageBreakInformationPacket Glaisher GlobalClusteringCoefficient GlobalPreferences GlobalSession Glow GoldenRatio GompertzMakehamDistribution GoodmanKruskalGamma GoodmanKruskalGammaTest Goto Grad Gradient GradientFilter GradientOrientationFilter Graph GraphAssortativity GraphCenter GraphComplement GraphData GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphElementData GraphEmbedding GraphHighlight GraphHighlightStyle GraphHub Graphics Graphics3D Graphics3DBox Graphics3DBoxOptions GraphicsArray GraphicsBaseline GraphicsBox GraphicsBoxOptions GraphicsColor GraphicsColumn GraphicsComplex GraphicsComplex3DBox GraphicsComplex3DBoxOptions GraphicsComplexBox GraphicsComplexBoxOptions GraphicsContents GraphicsData GraphicsGrid GraphicsGridBox GraphicsGroup GraphicsGroup3DBox GraphicsGroup3DBoxOptions GraphicsGroupBox GraphicsGroupBoxOptions GraphicsGrouping GraphicsHighlightColor GraphicsRow GraphicsSpacing GraphicsStyle GraphIntersection GraphLayout GraphLinkEfficiency GraphPeriphery GraphPlot GraphPlot3D GraphPower GraphPropertyDistribution GraphQ GraphRadius GraphReciprocity GraphRoot GraphStyle GraphUnion Gray GrayLevel GreatCircleDistance Greater GreaterEqual GreaterEqualLess GreaterFullEqual GreaterGreater GreaterLess GreaterSlantEqual GreaterTilde Green Grid GridBaseline GridBox GridBoxAlignment GridBoxBackground GridBoxDividers GridBoxFrame GridBoxItemSize GridBoxItemStyle GridBoxOptions GridBoxSpacings GridCreationSettings GridDefaultElement GridElementStyleOptions GridFrame GridFrameMargins GridGraph GridLines GridLinesStyle GroebnerBasis GroupActionBase GroupCentralizer GroupElementFromWord GroupElementPosition GroupElementQ GroupElements GroupElementToWord GroupGenerators GroupMultiplicationTable GroupOrbits GroupOrder GroupPageBreakWithin GroupSetwiseStabilizer GroupStabilizer GroupStabilizerChain Gudermannian GumbelDistribution HaarWavelet HadamardMatrix HalfNormalDistribution HamiltonianGraphQ HammingDistance HammingWindow HankelH1 HankelH2 HankelMatrix HannPoissonWindow HannWindow HaradaNortonGroupHN HararyGraph HarmonicMean HarmonicMeanFilter HarmonicNumber Hash HashTable Haversine HazardFunction Head HeadCompose Heads HeavisideLambda HeavisidePi HeavisideTheta HeldGroupHe HeldPart HelpBrowserLookup HelpBrowserNotebook HelpBrowserSettings HermiteDecomposition HermiteH HermitianMatrixQ HessenbergDecomposition Hessian HexadecimalCharacter Hexahedron HexahedronBox HexahedronBoxOptions HiddenSurface HighlightGraph HighlightImage HighpassFilter HigmanSimsGroupHS HilbertFilter HilbertMatrix Histogram Histogram3D HistogramDistribution HistogramList HistogramTransform HistogramTransformInterpolation HitMissTransform HITSCentrality HodgeDual HoeffdingD HoeffdingDTest Hold HoldAll HoldAllComplete HoldComplete HoldFirst HoldForm HoldPattern HoldRest HolidayCalendar HomeDirectory HomePage Horizontal HorizontalForm HorizontalGauge HorizontalScrollPosition HornerForm HotellingTSquareDistribution HoytDistribution HTMLSave Hue HumpDownHump HumpEqual HurwitzLerchPhi HurwitzZeta HyperbolicDistribution HypercubeGraph HyperexponentialDistribution Hyperfactorial Hypergeometric0F1 Hypergeometric0F1Regularized Hypergeometric1F1 Hypergeometric1F1Regularized Hypergeometric2F1 Hypergeometric2F1Regularized HypergeometricDistribution HypergeometricPFQ HypergeometricPFQRegularized HypergeometricU Hyperlink HyperlinkCreationSettings Hyphenation HyphenationOptions HypoexponentialDistribution HypothesisTestData I Identity IdentityMatrix If IgnoreCase Im Image Image3D Image3DSlices ImageAccumulate ImageAdd ImageAdjust ImageAlign ImageApply ImageAspectRatio ImageAssemble ImageCache ImageCacheValid ImageCapture ImageChannels ImageClip ImageColorSpace ImageCompose ImageConvolve ImageCooccurrence ImageCorners ImageCorrelate ImageCorrespondingPoints ImageCrop ImageData ImageDataPacket ImageDeconvolve ImageDemosaic ImageDifference ImageDimensions ImageDistance ImageEffect ImageFeatureTrack ImageFileApply ImageFileFilter ImageFileScan ImageFilter ImageForestingComponents ImageForwardTransformation ImageHistogram ImageKeypoints ImageLevels ImageLines ImageMargins ImageMarkers ImageMeasurements ImageMultiply ImageOffset ImagePad ImagePadding ImagePartition ImagePeriodogram ImagePerspectiveTransformation ImageQ ImageRangeCache ImageReflect ImageRegion ImageResize ImageResolution ImageRotate ImageRotated ImageScaled ImageScan ImageSize ImageSizeAction ImageSizeCache ImageSizeMultipliers ImageSizeRaw ImageSubtract ImageTake ImageTransformation ImageTrim ImageType ImageValue ImageValuePositions Implies Import ImportAutoReplacements ImportString ImprovementImportance In IncidenceGraph IncidenceList IncidenceMatrix IncludeConstantBasis IncludeFileExtension IncludePods IncludeSingularTerm Increment Indent IndentingNewlineSpacings IndentMaxFraction IndependenceTest IndependentEdgeSetQ IndependentUnit IndependentVertexSetQ Indeterminate IndexCreationOptions Indexed IndexGraph IndexTag Inequality InexactNumberQ InexactNumbers Infinity Infix Information Inherited InheritScope Initialization InitializationCell InitializationCellEvaluation InitializationCellWarning InlineCounterAssignments InlineCounterIncrements InlineRules Inner Inpaint Input InputAliases InputAssumptions InputAutoReplacements InputField InputFieldBox InputFieldBoxOptions InputForm InputGrouping InputNamePacket InputNotebook InputPacket InputSettings InputStream InputString InputStringPacket InputToBoxFormPacket Insert InsertionPointObject InsertResults Inset Inset3DBox Inset3DBoxOptions InsetBox InsetBoxOptions Install InstallService InString Integer IntegerDigits IntegerExponent IntegerLength IntegerPart IntegerPartitions IntegerQ Integers IntegerString Integral Integrate Interactive InteractiveTradingChart Interlaced Interleaving InternallyBalancedDecomposition InterpolatingFunction InterpolatingPolynomial Interpolation InterpolationOrder InterpolationPoints InterpolationPrecision Interpretation InterpretationBox InterpretationBoxOptions InterpretationFunction InterpretTemplate InterquartileRange Interrupt InterruptSettings Intersection Interval IntervalIntersection IntervalMemberQ IntervalUnion Inverse InverseBetaRegularized InverseCDF InverseChiSquareDistribution InverseContinuousWaveletTransform InverseDistanceTransform InverseEllipticNomeQ InverseErf InverseErfc InverseFourier InverseFourierCosTransform InverseFourierSequenceTransform InverseFourierSinTransform InverseFourierTransform InverseFunction InverseFunctions InverseGammaDistribution InverseGammaRegularized InverseGaussianDistribution InverseGudermannian InverseHaversine InverseJacobiCD InverseJacobiCN InverseJacobiCS InverseJacobiDC InverseJacobiDN InverseJacobiDS InverseJacobiNC InverseJacobiND InverseJacobiNS InverseJacobiSC InverseJacobiSD InverseJacobiSN InverseLaplaceTransform InversePermutation InverseRadon InverseSeries InverseSurvivalFunction InverseWaveletTransform InverseWeierstrassP InverseZTransform Invisible InvisibleApplication InvisibleTimes IrreduciblePolynomialQ IsolatingInterval IsomorphicGraphQ IsotopeData Italic Item ItemBox ItemBoxOptions ItemSize ItemStyle ItoProcess JaccardDissimilarity JacobiAmplitude Jacobian JacobiCD JacobiCN JacobiCS JacobiDC JacobiDN JacobiDS JacobiNC JacobiND JacobiNS JacobiP JacobiSC JacobiSD JacobiSN JacobiSymbol JacobiZeta JankoGroupJ1 JankoGroupJ2 JankoGroupJ3 JankoGroupJ4 JarqueBeraALMTest JohnsonDistribution Join Joined JoinedCurve JoinedCurveBox JoinForm JordanDecomposition JordanModelDecomposition K KagiChart KaiserBesselWindow KaiserWindow KalmanEstimator KalmanFilter KarhunenLoeveDecomposition KaryTree KatzCentrality KCoreComponents KDistribution KelvinBei KelvinBer KelvinKei KelvinKer KendallTau KendallTauTest KernelExecute KernelMixtureDistribution KernelObject Kernels Ket Khinchin KirchhoffGraph KirchhoffMatrix KleinInvariantJ KnightTourGraph KnotData KnownUnitQ KolmogorovSmirnovTest KroneckerDelta KroneckerModelDecomposition KroneckerProduct KroneckerSymbol KuiperTest KumaraswamyDistribution Kurtosis KuwaharaFilter Label Labeled LabeledSlider LabelingFunction LabelStyle LaguerreL LambdaComponents LambertW LanczosWindow LandauDistribution Language LanguageCategory LaplaceDistribution LaplaceTransform Laplacian LaplacianFilter LaplacianGaussianFilter Large Larger Last Latitude LatitudeLongitude LatticeData LatticeReduce Launch LaunchKernels LayeredGraphPlot LayerSizeFunction LayoutInformation LCM LeafCount LeapYearQ LeastSquares LeastSquaresFilterKernel Left LeftArrow LeftArrowBar LeftArrowRightArrow LeftDownTeeVector LeftDownVector LeftDownVectorBar LeftRightArrow LeftRightVector LeftTee LeftTeeArrow LeftTeeVector LeftTriangle LeftTriangleBar LeftTriangleEqual LeftUpDownVector LeftUpTeeVector LeftUpVector LeftUpVectorBar LeftVector LeftVectorBar LegendAppearance Legended LegendFunction LegendLabel LegendLayout LegendMargins LegendMarkers LegendMarkerSize LegendreP LegendreQ LegendreType Length LengthWhile LerchPhi Less LessEqual LessEqualGreater LessFullEqual LessGreater LessLess LessSlantEqual LessTilde LetterCharacter LetterQ Level LeveneTest LeviCivitaTensor LevyDistribution Lexicographic LibraryFunction LibraryFunctionError LibraryFunctionInformation LibraryFunctionLoad LibraryFunctionUnload LibraryLoad LibraryUnload LicenseID LiftingFilterData LiftingWaveletTransform LightBlue LightBrown LightCyan Lighter LightGray LightGreen Lighting LightingAngle LightMagenta LightOrange LightPink LightPurple LightRed LightSources LightYellow Likelihood Limit LimitsPositioning LimitsPositioningTokens LindleyDistribution Line Line3DBox LinearFilter LinearFractionalTransform LinearModelFit LinearOffsetFunction LinearProgramming LinearRecurrence LinearSolve LinearSolveFunction LineBox LineBreak LinebreakAdjustments LineBreakChart LineBreakWithin LineColor LineForm LineGraph LineIndent LineIndentMaxFraction LineIntegralConvolutionPlot LineIntegralConvolutionScale LineLegend LineOpacity LineSpacing LineWrapParts LinkActivate LinkClose LinkConnect LinkConnectedQ LinkCreate LinkError LinkFlush LinkFunction LinkHost LinkInterrupt LinkLaunch LinkMode LinkObject LinkOpen LinkOptions LinkPatterns LinkProtocol LinkRead LinkReadHeld LinkReadyQ Links LinkWrite LinkWriteHeld LiouvilleLambda List Listable ListAnimate ListContourPlot ListContourPlot3D ListConvolve ListCorrelate ListCurvePathPlot ListDeconvolve ListDensityPlot Listen ListFourierSequenceTransform ListInterpolation ListLineIntegralConvolutionPlot ListLinePlot ListLogLinearPlot ListLogLogPlot ListLogPlot ListPicker ListPickerBox ListPickerBoxBackground ListPickerBoxOptions ListPlay ListPlot ListPlot3D ListPointPlot3D ListPolarPlot ListQ ListStreamDensityPlot ListStreamPlot ListSurfacePlot3D ListVectorDensityPlot ListVectorPlot ListVectorPlot3D ListZTransform Literal LiteralSearch LocalClusteringCoefficient LocalizeVariables LocationEquivalenceTest LocationTest Locator LocatorAutoCreate LocatorBox LocatorBoxOptions LocatorCentering LocatorPane LocatorPaneBox LocatorPaneBoxOptions LocatorRegion Locked Log Log10 Log2 LogBarnesG LogGamma LogGammaDistribution LogicalExpand LogIntegral LogisticDistribution LogitModelFit LogLikelihood LogLinearPlot LogLogisticDistribution LogLogPlot LogMultinormalDistribution LogNormalDistribution LogPlot LogRankTest LogSeriesDistribution LongEqual Longest LongestAscendingSequence LongestCommonSequence LongestCommonSequencePositions LongestCommonSubsequence LongestCommonSubsequencePositions LongestMatch LongForm Longitude LongLeftArrow LongLeftRightArrow LongRightArrow Loopback LoopFreeGraphQ LowerCaseQ LowerLeftArrow LowerRightArrow LowerTriangularize LowpassFilter LQEstimatorGains LQGRegulator LQOutputRegulatorGains LQRegulatorGains LUBackSubstitution LucasL LuccioSamiComponents LUDecomposition LyapunovSolve LyonsGroupLy MachineID MachineName MachineNumberQ MachinePrecision MacintoshSystemPageSetup Magenta Magnification Magnify MainSolve MaintainDynamicCaches Majority MakeBoxes MakeExpression MakeRules MangoldtLambda ManhattanDistance Manipulate Manipulator MannWhitneyTest MantissaExponent Manual Map MapAll MapAt MapIndexed MAProcess MapThread MarcumQ MardiaCombinedTest MardiaKurtosisTest MardiaSkewnessTest MarginalDistribution MarkovProcessProperties Masking MatchingDissimilarity MatchLocalNameQ MatchLocalNames MatchQ Material MathematicaNotation MathieuC MathieuCharacteristicA MathieuCharacteristicB MathieuCharacteristicExponent MathieuCPrime MathieuGroupM11 MathieuGroupM12 MathieuGroupM22 MathieuGroupM23 MathieuGroupM24 MathieuS MathieuSPrime MathMLForm MathMLText Matrices MatrixExp MatrixForm MatrixFunction MatrixLog MatrixPlot MatrixPower MatrixQ MatrixRank Max MaxBend MaxDetect MaxExtraBandwidths MaxExtraConditions MaxFeatures MaxFilter Maximize MaxIterations MaxMemoryUsed MaxMixtureKernels MaxPlotPoints MaxPoints MaxRecursion MaxStableDistribution MaxStepFraction MaxSteps MaxStepSize MaxValue MaxwellDistribution McLaughlinGroupMcL Mean MeanClusteringCoefficient MeanDegreeConnectivity MeanDeviation MeanFilter MeanGraphDistance MeanNeighborDegree MeanShift MeanShiftFilter Median MedianDeviation MedianFilter Medium MeijerG MeixnerDistribution MemberQ MemoryConstrained MemoryInUse Menu MenuAppearance MenuCommandKey MenuEvaluator MenuItem MenuPacket MenuSortingValue MenuStyle MenuView MergeDifferences Mesh MeshFunctions MeshRange MeshShading MeshStyle Message MessageDialog MessageList MessageName MessageOptions MessagePacket Messages MessagesNotebook MetaCharacters MetaInformation Method MethodOptions MexicanHatWavelet MeyerWavelet Min MinDetect MinFilter MinimalPolynomial MinimalStateSpaceModel Minimize Minors MinRecursion MinSize MinStableDistribution Minus MinusPlus MinValue Missing MissingDataMethod MittagLefflerE MixedRadix MixedRadixQuantity MixtureDistribution Mod Modal Mode Modular ModularLambda Module Modulus MoebiusMu Moment Momentary MomentConvert MomentEvaluate MomentGeneratingFunction Monday Monitor MonomialList MonomialOrder MonsterGroupM MorletWavelet MorphologicalBinarize MorphologicalBranchPoints MorphologicalComponents MorphologicalEulerNumber MorphologicalGraph MorphologicalPerimeter MorphologicalTransform Most MouseAnnotation MouseAppearance MouseAppearanceTag MouseButtons Mouseover MousePointerNote MousePosition MovingAverage MovingMedian MoyalDistribution MultiedgeStyle MultilaunchWarning MultiLetterItalics MultiLetterStyle MultilineFunction Multinomial MultinomialDistribution MultinormalDistribution MultiplicativeOrder Multiplicity Multiselection MultivariateHypergeometricDistribution MultivariatePoissonDistribution MultivariateTDistribution N NakagamiDistribution NameQ Names NamespaceBox Nand NArgMax NArgMin NBernoulliB NCache NDSolve NDSolveValue Nearest NearestFunction NeedCurrentFrontEndPackagePacket NeedCurrentFrontEndSymbolsPacket NeedlemanWunschSimilarity Needs Negative NegativeBinomialDistribution NegativeMultinomialDistribution NeighborhoodGraph Nest NestedGreaterGreater NestedLessLess NestedScriptRules NestList NestWhile NestWhileList NevilleThetaC NevilleThetaD NevilleThetaN NevilleThetaS NewPrimitiveStyle NExpectation Next NextPrime NHoldAll NHoldFirst NHoldRest NicholsGridLines NicholsPlot NIntegrate NMaximize NMaxValue NMinimize NMinValue NominalVariables NonAssociative NoncentralBetaDistribution NoncentralChiSquareDistribution NoncentralFRatioDistribution NoncentralStudentTDistribution NonCommutativeMultiply NonConstants None NonlinearModelFit NonlocalMeansFilter NonNegative NonPositive Nor NorlundB Norm Normal NormalDistribution NormalGrouping Normalize NormalizedSquaredEuclideanDistance NormalsFunction NormFunction Not NotCongruent NotCupCap NotDoubleVerticalBar Notebook NotebookApply NotebookAutoSave NotebookClose NotebookConvertSettings NotebookCreate NotebookCreateReturnObject NotebookDefault NotebookDelete NotebookDirectory NotebookDynamicExpression NotebookEvaluate NotebookEventActions NotebookFileName NotebookFind NotebookFindReturnObject NotebookGet NotebookGetLayoutInformationPacket NotebookGetMisspellingsPacket NotebookInformation NotebookInterfaceObject NotebookLocate NotebookObject NotebookOpen NotebookOpenReturnObject NotebookPath NotebookPrint NotebookPut NotebookPutReturnObject NotebookRead NotebookResetGeneratedCells Notebooks NotebookSave NotebookSaveAs NotebookSelection NotebookSetupLayoutInformationPacket NotebooksMenu NotebookWrite NotElement NotEqualTilde NotExists NotGreater NotGreaterEqual NotGreaterFullEqual NotGreaterGreater NotGreaterLess NotGreaterSlantEqual NotGreaterTilde NotHumpDownHump NotHumpEqual NotLeftTriangle NotLeftTriangleBar NotLeftTriangleEqual NotLess NotLessEqual NotLessFullEqual NotLessGreater NotLessLess NotLessSlantEqual NotLessTilde NotNestedGreaterGreater NotNestedLessLess NotPrecedes NotPrecedesEqual NotPrecedesSlantEqual NotPrecedesTilde NotReverseElement NotRightTriangle NotRightTriangleBar NotRightTriangleEqual NotSquareSubset NotSquareSubsetEqual NotSquareSuperset NotSquareSupersetEqual NotSubset NotSubsetEqual NotSucceeds NotSucceedsEqual NotSucceedsSlantEqual NotSucceedsTilde NotSuperset NotSupersetEqual NotTilde NotTildeEqual NotTildeFullEqual NotTildeTilde NotVerticalBar NProbability NProduct NProductFactors NRoots NSolve NSum NSumTerms Null NullRecords NullSpace NullWords Number NumberFieldClassNumber NumberFieldDiscriminant NumberFieldFundamentalUnits NumberFieldIntegralBasis NumberFieldNormRepresentatives NumberFieldRegulator NumberFieldRootsOfUnity NumberFieldSignature NumberForm NumberFormat NumberMarks NumberMultiplier NumberPadding NumberPoint NumberQ NumberSeparator NumberSigns NumberString Numerator NumericFunction NumericQ NuttallWindow NValues NyquistGridLines NyquistPlot O ObservabilityGramian ObservabilityMatrix ObservableDecomposition ObservableModelQ OddQ Off Offset OLEData On ONanGroupON OneIdentity Opacity Open OpenAppend Opener OpenerBox OpenerBoxOptions OpenerView OpenFunctionInspectorPacket Opening OpenRead OpenSpecialOptions OpenTemporary OpenWrite Operate OperatingSystem OptimumFlowData Optional OptionInspectorSettings OptionQ Options OptionsPacket OptionsPattern OptionValue OptionValueBox OptionValueBoxOptions Or Orange Order OrderDistribution OrderedQ Ordering Orderless OrnsteinUhlenbeckProcess Orthogonalize Out Outer OutputAutoOverwrite OutputControllabilityMatrix OutputControllableModelQ OutputForm OutputFormData OutputGrouping OutputMathEditExpression OutputNamePacket OutputResponse OutputSizeLimit OutputStream Over OverBar OverDot Overflow OverHat Overlaps Overlay OverlayBox OverlayBoxOptions Overscript OverscriptBox OverscriptBoxOptions OverTilde OverVector OwenT OwnValues PackingMethod PaddedForm Padding PadeApproximant PadLeft PadRight PageBreakAbove PageBreakBelow PageBreakWithin PageFooterLines PageFooters PageHeaderLines PageHeaders PageHeight PageRankCentrality PageWidth PairedBarChart PairedHistogram PairedSmoothHistogram PairedTTest PairedZTest PaletteNotebook PalettePath Pane PaneBox PaneBoxOptions Panel PanelBox PanelBoxOptions Paneled PaneSelector PaneSelectorBox PaneSelectorBoxOptions PaperWidth ParabolicCylinderD ParagraphIndent ParagraphSpacing ParallelArray ParallelCombine ParallelDo ParallelEvaluate Parallelization Parallelize ParallelMap ParallelNeeds ParallelProduct ParallelSubmit ParallelSum ParallelTable ParallelTry Parameter ParameterEstimator ParameterMixtureDistribution ParameterVariables ParametricFunction ParametricNDSolve ParametricNDSolveValue ParametricPlot ParametricPlot3D ParentConnect ParentDirectory ParentForm Parenthesize ParentList ParetoDistribution Part PartialCorrelationFunction PartialD ParticleData Partition PartitionsP PartitionsQ ParzenWindow PascalDistribution PassEventsDown PassEventsUp Paste PasteBoxFormInlineCells PasteButton Path PathGraph PathGraphQ Pattern PatternSequence PatternTest PauliMatrix PaulWavelet Pause PausedTime PDF PearsonChiSquareTest PearsonCorrelationTest PearsonDistribution PerformanceGoal PeriodicInterpolation Periodogram PeriodogramArray PermutationCycles PermutationCyclesQ PermutationGroup PermutationLength PermutationList PermutationListQ PermutationMax PermutationMin PermutationOrder PermutationPower PermutationProduct PermutationReplace Permutations PermutationSupport Permute PeronaMalikFilter Perpendicular PERTDistribution PetersenGraph PhaseMargins Pi Pick PIDData PIDDerivativeFilter PIDFeedforward PIDTune Piecewise PiecewiseExpand PieChart PieChart3D PillaiTrace PillaiTraceTest Pink Pivoting PixelConstrained PixelValue PixelValuePositions Placed Placeholder PlaceholderReplace Plain PlanarGraphQ Play PlayRange Plot Plot3D Plot3Matrix PlotDivision PlotJoined PlotLabel PlotLayout PlotLegends PlotMarkers PlotPoints PlotRange PlotRangeClipping PlotRangePadding PlotRegion PlotStyle Plus PlusMinus Pochhammer PodStates PodWidth Point Point3DBox PointBox PointFigureChart PointForm PointLegend PointSize PoissonConsulDistribution PoissonDistribution PoissonProcess PoissonWindow PolarAxes PolarAxesOrigin PolarGridLines PolarPlot PolarTicks PoleZeroMarkers PolyaAeppliDistribution PolyGamma Polygon Polygon3DBox Polygon3DBoxOptions PolygonBox PolygonBoxOptions PolygonHoleScale PolygonIntersections PolygonScale PolyhedronData PolyLog PolynomialExtendedGCD PolynomialForm PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialQuotientRemainder PolynomialReduce PolynomialRemainder Polynomials PopupMenu PopupMenuBox PopupMenuBoxOptions PopupView PopupWindow Position Positive PositiveDefiniteMatrixQ PossibleZeroQ Postfix PostScript Power PowerDistribution PowerExpand PowerMod PowerModList PowerSpectralDensity PowersRepresentations PowerSymmetricPolynomial Precedence PrecedenceForm Precedes PrecedesEqual PrecedesSlantEqual PrecedesTilde Precision PrecisionGoal PreDecrement PredictionRoot PreemptProtect PreferencesPath Prefix PreIncrement Prepend PrependTo PreserveImageOptions Previous PriceGraphDistribution PrimaryPlaceholder Prime PrimeNu PrimeOmega PrimePi PrimePowerQ PrimeQ Primes PrimeZetaP PrimitiveRoot PrincipalComponents PrincipalValue Print PrintAction PrintForm PrintingCopies PrintingOptions PrintingPageRange PrintingStartingPageNumber PrintingStyleEnvironment PrintPrecision PrintTemporary Prism PrismBox PrismBoxOptions PrivateCellOptions PrivateEvaluationOptions PrivateFontOptions PrivateFrontEndOptions PrivateNotebookOptions PrivatePaths Probability ProbabilityDistribution ProbabilityPlot ProbabilityPr ProbabilityScalePlot ProbitModelFit ProcessEstimator ProcessParameterAssumptions ProcessParameterQ ProcessStateDomain ProcessTimeDomain Product ProductDistribution ProductLog ProgressIndicator ProgressIndicatorBox ProgressIndicatorBoxOptions Projection Prolog PromptForm Properties Property PropertyList PropertyValue Proportion Proportional Protect Protected ProteinData Pruning PseudoInverse Purple Put PutAppend Pyramid PyramidBox PyramidBoxOptions QBinomial QFactorial QGamma QHypergeometricPFQ QPochhammer QPolyGamma QRDecomposition QuadraticIrrationalQ Quantile QuantilePlot Quantity QuantityForm QuantityMagnitude QuantityQ QuantityUnit Quartics QuartileDeviation Quartiles QuartileSkewness QueueingNetworkProcess QueueingProcess QueueProperties Quiet Quit Quotient QuotientRemainder RadialityCentrality RadicalBox RadicalBoxOptions RadioButton RadioButtonBar RadioButtonBox RadioButtonBoxOptions Radon RamanujanTau RamanujanTauL RamanujanTauTheta RamanujanTauZ Random RandomChoice RandomComplex RandomFunction RandomGraph RandomImage RandomInteger RandomPermutation RandomPrime RandomReal RandomSample RandomSeed RandomVariate RandomWalkProcess Range RangeFilter RangeSpecification RankedMax RankedMin Raster Raster3D Raster3DBox Raster3DBoxOptions RasterArray RasterBox RasterBoxOptions Rasterize RasterSize Rational RationalFunctions Rationalize Rationals Ratios Raw RawArray RawBoxes RawData RawMedium RayleighDistribution Re Read ReadList ReadProtected Real RealBlockDiagonalForm RealDigits RealExponent Reals Reap Record RecordLists RecordSeparators Rectangle RectangleBox RectangleBoxOptions RectangleChart RectangleChart3D RecurrenceFilter RecurrenceTable RecurringDigitsForm Red Reduce RefBox ReferenceLineStyle ReferenceMarkers ReferenceMarkerStyle Refine ReflectionMatrix ReflectionTransform Refresh RefreshRate RegionBinarize RegionFunction RegionPlot RegionPlot3D RegularExpression Regularization Reinstall Release ReleaseHold ReliabilityDistribution ReliefImage ReliefPlot Remove RemoveAlphaChannel RemoveAsynchronousTask Removed RemoveInputStreamMethod RemoveOutputStreamMethod RemoveProperty RemoveScheduledTask RenameDirectory RenameFile RenderAll RenderingOptions RenewalProcess RenkoChart Repeated RepeatedNull RepeatedString Replace ReplaceAll ReplaceHeldPart ReplaceImageValue ReplaceList ReplacePart ReplacePixelValue ReplaceRepeated Resampling Rescale RescalingTransform ResetDirectory ResetMenusPacket ResetScheduledTask Residue Resolve Rest Resultant ResumePacket Return ReturnExpressionPacket ReturnInputFormPacket ReturnPacket ReturnTextPacket Reverse ReverseBiorthogonalSplineWavelet ReverseElement ReverseEquilibrium ReverseGraph ReverseUpEquilibrium RevolutionAxis RevolutionPlot3D RGBColor RiccatiSolve RiceDistribution RidgeFilter RiemannR RiemannSiegelTheta RiemannSiegelZ Riffle Right RightArrow RightArrowBar RightArrowLeftArrow RightCosetRepresentative RightDownTeeVector RightDownVector RightDownVectorBar RightTee RightTeeArrow RightTeeVector RightTriangle RightTriangleBar RightTriangleEqual RightUpDownVector RightUpTeeVector RightUpVector RightUpVectorBar RightVector RightVectorBar RiskAchievementImportance RiskReductionImportance RogersTanimotoDissimilarity Root RootApproximant RootIntervals RootLocusPlot RootMeanSquare RootOfUnityQ RootReduce Roots RootSum Rotate RotateLabel RotateLeft RotateRight RotationAction RotationBox RotationBoxOptions RotationMatrix RotationTransform Round RoundImplies RoundingRadius Row RowAlignments RowBackgrounds RowBox RowHeights RowLines RowMinHeight RowReduce RowsEqual RowSpacings RSolve RudvalisGroupRu Rule RuleCondition RuleDelayed RuleForm RulerUnits Run RunScheduledTask RunThrough RuntimeAttributes RuntimeOptions RussellRaoDissimilarity SameQ SameTest SampleDepth SampledSoundFunction SampledSoundList SampleRate SamplingPeriod SARIMAProcess SARMAProcess SatisfiabilityCount SatisfiabilityInstances SatisfiableQ Saturday Save Saveable SaveAutoDelete SaveDefinitions SawtoothWave Scale Scaled ScaleDivisions ScaledMousePosition ScaleOrigin ScalePadding ScaleRanges ScaleRangeStyle ScalingFunctions ScalingMatrix ScalingTransform Scan ScheduledTaskActiveQ ScheduledTaskData ScheduledTaskObject ScheduledTasks SchurDecomposition ScientificForm ScreenRectangle ScreenStyleEnvironment ScriptBaselineShifts ScriptLevel ScriptMinSize ScriptRules ScriptSizeMultipliers Scrollbars ScrollingOptions ScrollPosition Sec Sech SechDistribution SectionGrouping SectorChart SectorChart3D SectorOrigin SectorSpacing SeedRandom Select Selectable SelectComponents SelectedCells SelectedNotebook Selection SelectionAnimate SelectionCell SelectionCellCreateCell SelectionCellDefaultStyle SelectionCellParentStyle SelectionCreateCell SelectionDebuggerTag SelectionDuplicateCell SelectionEvaluate SelectionEvaluateCreateCell SelectionMove SelectionPlaceholder SelectionSetStyle SelectWithContents SelfLoops SelfLoopStyle SemialgebraicComponentInstances SendMail Sequence SequenceAlignment SequenceForm SequenceHold SequenceLimit Series SeriesCoefficient SeriesData SessionTime Set SetAccuracy SetAlphaChannel SetAttributes Setbacks SetBoxFormNamesPacket SetDelayed SetDirectory SetEnvironment SetEvaluationNotebook SetFileDate SetFileLoadingContext SetNotebookStatusLine SetOptions SetOptionsPacket SetPrecision SetProperty SetSelectedNotebook SetSharedFunction SetSharedVariable SetSpeechParametersPacket SetStreamPosition SetSystemOptions Setter SetterBar SetterBox SetterBoxOptions Setting SetValue Shading Shallow ShannonWavelet ShapiroWilkTest Share Sharpen ShearingMatrix ShearingTransform ShenCastanMatrix Short ShortDownArrow Shortest ShortestMatch ShortestPathFunction ShortLeftArrow ShortRightArrow ShortUpArrow Show ShowAutoStyles ShowCellBracket ShowCellLabel ShowCellTags ShowClosedCellArea ShowContents ShowControls ShowCursorTracker ShowGroupOpenCloseIcon ShowGroupOpener ShowInvisibleCharacters ShowPageBreaks ShowPredictiveInterface ShowSelection ShowShortBoxForm ShowSpecialCharacters ShowStringCharacters ShowSyntaxStyles ShrinkingDelay ShrinkWrapBoundingBox SiegelTheta SiegelTukeyTest Sign Signature SignedRankTest SignificanceLevel SignPadding SignTest SimilarityRules SimpleGraph SimpleGraphQ Simplify Sin Sinc SinghMaddalaDistribution SingleEvaluation SingleLetterItalics SingleLetterStyle SingularValueDecomposition SingularValueList SingularValuePlot SingularValues Sinh SinhIntegral SinIntegral SixJSymbol Skeleton SkeletonTransform SkellamDistribution Skewness SkewNormalDistribution Skip SliceDistribution Slider Slider2D Slider2DBox Slider2DBoxOptions SliderBox SliderBoxOptions SlideView Slot SlotSequence Small SmallCircle Smaller SmithDelayCompensator SmithWatermanSimilarity SmoothDensityHistogram SmoothHistogram SmoothHistogram3D SmoothKernelDistribution SocialMediaData Socket SokalSneathDissimilarity Solve SolveAlways SolveDelayed Sort SortBy Sound SoundAndGraphics SoundNote SoundVolume Sow Space SpaceForm Spacer Spacings Span SpanAdjustments SpanCharacterRounding SpanFromAbove SpanFromBoth SpanFromLeft SpanLineThickness SpanMaxSize SpanMinSize SpanningCharacters SpanSymmetric SparseArray SpatialGraphDistribution Speak SpeakTextPacket SpearmanRankTest SpearmanRho Spectrogram SpectrogramArray Specularity SpellingCorrection SpellingDictionaries SpellingDictionariesPath SpellingOptions SpellingSuggestionsPacket Sphere SphereBox SphericalBesselJ SphericalBesselY SphericalHankelH1 SphericalHankelH2 SphericalHarmonicY SphericalPlot3D SphericalRegion SpheroidalEigenvalue SpheroidalJoiningFactor SpheroidalPS SpheroidalPSPrime SpheroidalQS SpheroidalQSPrime SpheroidalRadialFactor SpheroidalS1 SpheroidalS1Prime SpheroidalS2 SpheroidalS2Prime Splice SplicedDistribution SplineClosed SplineDegree SplineKnots SplineWeights Split SplitBy SpokenString Sqrt SqrtBox SqrtBoxOptions Square SquaredEuclideanDistance SquareFreeQ SquareIntersection SquaresR SquareSubset SquareSubsetEqual SquareSuperset SquareSupersetEqual SquareUnion SquareWave StabilityMargins StabilityMarginsStyle StableDistribution Stack StackBegin StackComplete StackInhibit StandardDeviation StandardDeviationFilter StandardForm Standardize StandbyDistribution Star StarGraph StartAsynchronousTask StartingStepSize StartOfLine StartOfString StartScheduledTask StartupSound StateDimensions StateFeedbackGains StateOutputEstimator StateResponse StateSpaceModel StateSpaceRealization StateSpaceTransform StationaryDistribution StationaryWaveletPacketTransform StationaryWaveletTransform StatusArea StatusCentrality StepMonitor StieltjesGamma StirlingS1 StirlingS2 StopAsynchronousTask StopScheduledTask StrataVariables StratonovichProcess StreamColorFunction StreamColorFunctionScaling StreamDensityPlot StreamPlot StreamPoints StreamPosition Streams StreamScale StreamStyle String StringBreak StringByteCount StringCases StringCount StringDrop StringExpression StringForm StringFormat StringFreeQ StringInsert StringJoin StringLength StringMatchQ StringPosition StringQ StringReplace StringReplaceList StringReplacePart StringReverse StringRotateLeft StringRotateRight StringSkeleton StringSplit StringTake StringToStream StringTrim StripBoxes StripOnInput StripWrapperBoxes StrokeForm StructuralImportance StructuredArray StructuredSelection StruveH StruveL Stub StudentTDistribution Style StyleBox StyleBoxAutoDelete StyleBoxOptions StyleData StyleDefinitions StyleForm StyleKeyMapping StyleMenuListing StyleNameDialogSettings StyleNames StylePrint StyleSheetPath Subfactorial Subgraph SubMinus SubPlus SubresultantPolynomialRemainders SubresultantPolynomials Subresultants Subscript SubscriptBox SubscriptBoxOptions Subscripted Subset SubsetEqual Subsets SubStar Subsuperscript SubsuperscriptBox SubsuperscriptBoxOptions Subtract SubtractFrom SubValues Succeeds SucceedsEqual SucceedsSlantEqual SucceedsTilde SuchThat Sum SumConvergence Sunday SuperDagger SuperMinus SuperPlus Superscript SuperscriptBox SuperscriptBoxOptions Superset SupersetEqual SuperStar Surd SurdForm SurfaceColor SurfaceGraphics SurvivalDistribution SurvivalFunction SurvivalModel SurvivalModelFit SuspendPacket SuzukiDistribution SuzukiGroupSuz SwatchLegend Switch Symbol SymbolName SymletWavelet Symmetric SymmetricGroup SymmetricMatrixQ SymmetricPolynomial SymmetricReduction Symmetrize SymmetrizedArray SymmetrizedArrayRules SymmetrizedDependentComponents SymmetrizedIndependentComponents SymmetrizedReplacePart SynchronousInitialization SynchronousUpdating Syntax SyntaxForm SyntaxInformation SyntaxLength SyntaxPacket SyntaxQ SystemDialogInput SystemException SystemHelpPath SystemInformation SystemInformationData SystemOpen SystemOptions SystemsModelDelay SystemsModelDelayApproximate SystemsModelDelete SystemsModelDimensions SystemsModelExtract SystemsModelFeedbackConnect SystemsModelLabels SystemsModelOrder SystemsModelParallelConnect SystemsModelSeriesConnect SystemsModelStateFeedbackConnect SystemStub Tab TabFilling Table TableAlignments TableDepth TableDirections TableForm TableHeadings TableSpacing TableView TableViewBox TabSpacings TabView TabViewBox TabViewBoxOptions TagBox TagBoxNote TagBoxOptions TaggingRules TagSet TagSetDelayed TagStyle TagUnset Take TakeWhile Tally Tan Tanh TargetFunctions TargetUnits TautologyQ TelegraphProcess TemplateBox TemplateBoxOptions TemplateSlotSequence TemporalData Temporary TemporaryVariable TensorContract TensorDimensions TensorExpand TensorProduct TensorQ TensorRank TensorReduce TensorSymmetry TensorTranspose TensorWedge Tetrahedron TetrahedronBox TetrahedronBoxOptions TeXForm TeXSave Text Text3DBox Text3DBoxOptions TextAlignment TextBand TextBoundingBox TextBox TextCell TextClipboardType TextData TextForm TextJustification TextLine TextPacket TextParagraph TextRecognize TextRendering TextStyle Texture TextureCoordinateFunction TextureCoordinateScaling Therefore ThermometerGauge Thick Thickness Thin Thinning ThisLink ThompsonGroupTh Thread ThreeJSymbol Threshold Through Throw Thumbnail Thursday Ticks TicksStyle Tilde TildeEqual TildeFullEqual TildeTilde TimeConstrained TimeConstraint Times TimesBy TimeSeriesForecast TimeSeriesInvertibility TimeUsed TimeValue TimeZone Timing Tiny 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+$( document ).ready(function() {
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+Copyright (c) 2006, Ivan Sagalaev
+All rights reserved.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ * Neither the name of highlight.js nor the names of its contributors
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+ without specific prior written permission.
+
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+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE REGENTS AND CONTRIBUTORS BE LIABLE FOR ANY
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+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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+
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+ Sorry, page not found.
+ </div>
+
+{% endblock %}
--- /dev/null
+<div role="search">
+ <form id ="rtd-search-form" class="wy-form" action="{{ base_url }}/search.html" method="get">
+ <input type="text" name="q" placeholder="Search docs" />
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+</div>
--- /dev/null
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+
+ {% for nav_item in nav_item.children %}
+ {% include 'toc.html' %}
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+{% endif %}
--- /dev/null
+<div class="rst-versions" role="note" style="cursor: pointer">
+ <span class="rst-current-version" data-toggle="rst-current-version">
+ {% if repo_name == 'GitHub' %}
+ <a class="icon icon-github" style="float: left; color: #fcfcfc"> GitHub</a>
+ {% elif repo_name == 'Bitbucket' %}
+ <a class="icon icon-bitbucket" style="float: left; color: #fcfcfc"> BitBucket</a>
+ {% endif %}
+ {% if previous_page %}
+ <span><a href="{{ previous_page.url }}" style="color: #fcfcfc;">« Previous</a></span>
+ {% endif %}
+ {% if next_page %}
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+ {% endif %}
+ </span>
+</div>
--- /dev/null
+python-markdown-math
--- /dev/null
+site_name: NLopt Documentation
+site_author: S. G. Johnson et al.
+repo_url: https://github.com/stevengj/NLopt/
+
+docs_dir: 'doc/docs'
+site_dir: 'doc/site'
+
+theme_dir: 'doc/nlopt-mkdocs-theme'
+theme: readthedocs
+
+python:
+ version: 2 # for unicode
+ setup_py_install: True
+
+markdown_extensions:
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+ - toc:
+ title: Table of Contents
+ - attr_list
+ - fenced_code
+ - mdx_math:
+ enable_dollar_delimiter: True
+
+extra_javascript: ['https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML','mathjaxhelper.js']
+
+pages:
+ - NLopt:
+ - Overview: index.md
+ - Release Notes: NLopt_release_notes.md
+ - FAQ: NLopt_FAQ.md
+ - NLopt manual:
+ - NLopt manual: NLopt_manual.md
+ - Introduction: NLopt_Introduction.md
+ - Installation: NLopt_Installation.md
+ - Tutorial: NLopt_Tutorial.md
+ - NLopt reference:
+ - General reference: NLopt_Reference.md
+ - C++ reference: NLopt_C-plus-plus_Reference.md
+ - Fortran reference: NLopt_Fortran_Reference.md
+ - Matlab reference: NLopt_Matlab_Reference.md
+ - Python reference: NLopt_Python_Reference.md
+ - Guile reference: NLopt_Guile_Reference.md
+ - R reference: NLopt_R_Reference.md
+ - Deprecated API reference: NLopt_Deprecated_API_Reference.md
+ - NLopt algorithms:
+ - NLopt algorithms: NLopt_Algorithms.md
+ - NLopt on Windows: NLopt_on_Windows.md
+ - License and Copyright: NLopt_License_and_Copyright.md
+ - Citing NLopt: Citing_NLopt.md
~ianmdlvl / nlopt.git / commitdiff
