.BI " nlopt_func " "f" ,
.BI " void* " "f_data" ,
.BI " int " "m" ,
-.BI " nlopt_func " "c" ,
+.BI " nlopt_func " "fc" ,
.BI " void* " "fc_data" ,
.BI " ptrdiff_t " "fc_datum_size" ,
.BI " const double* " "lb" ,
.IR f ,
and other algorithms do not require derivatives. Some of the
algorithms attempt to find a global minimum within the given bounds,
-and others find only a local minimum. Some of the algorithms can handle
-nonlinear constraints, but most of the algorithms only handle the
+and others find only a local minimum. Most of the algorithms only handle the
case where
.I m
-is zero (no explicit nonlinear constraints).
+is zero (no explicit nonlinear constraints); the only algorithms that
+currently support positive
+.I m
+are
+.B NLOPT_LD_MMA
+and
+.BR NLOPT_LN_COBYLA .
.PP
The
.B nlopt_minimize_constrained
.I m
is currently only supported by the
.B NLOPT_LD_MMA
-algorithm below.
+and
+.B NLOPT_LN_COBYLA
+algorithms below.
.sp
In particular, the nonlinear constraints are of the form
\fIfc\fR(\fIx\fR) <= 0, where the function
.sp
In particular, the constraint function
.I fc
-will be called
+will be called (at most)
.I m
times for each
.IR x ,
-and the i-th constraint (0 <= i <=
+and the i-th constraint (0 <= i <
.IR m )
will be passed an
.I fc_datum
.I fc
function would be called
.I m
-times for each point, and be passed data[0] through data[m-1] in sequence.
+times for each point, and be passed &data[0] through &data[m-1] in sequence.
.SH ALGORITHMS
The
.I algorithm
al. to be more weighted towards local search. Does not support
unconstrainted optimization. There are also several other variants of
the DIRECT algorithm that are supported:
-.BR NLOPT_GLOBAL_DIRECT ,
+.BR NLOPT_GN_DIRECT ,
which is the original DIRECT algorithm;
-.BR NLOPT_GLOBAL_DIRECT_L_RAND ,
+.BR NLOPT_GN_DIRECT_L_RAND ,
a slightly randomized version of DIRECT-L that may be better in
high-dimensional search spaces;
-.BR NLOPT_GLOBAL_DIRECT_NOSCAL ,
-.BR NLOPT_GLOBAL_DIRECT_L_NOSCAL ,
+.BR NLOPT_GN_DIRECT_NOSCAL ,
+.BR NLOPT_GN_DIRECT_L_NOSCAL ,
and
-.BR NLOPT_GLOBAL_DIRECT_L_RAND_NOSCAL ,
+.BR NLOPT_GN_DIRECT_L_RAND_NOSCAL ,
which are versions of DIRECT where the dimensions are not rescaled to
a unit hypercube (which means that dimensions with larger bounds are
given more weight).
and should be linked via -lnlopt_cxx (via a C++ compiler, in order
to link the C++ standard libraries).
.TP
-.B NLOPT_LN_SUBPLEX
+.B NLOPT_LN_NELDERMEAD
Perform a local (L) derivative-free (N) optimization, starting at
.IR x ,
-using the Subplex algorithm of Rowan et al., which is an improved
-variant of Nelder-Mead simplex algorithm. (Like Nelder-Mead, Subplex
-often works well in practice, even for discontinuous objectives, but
-there is no rigorous guarantee that it will converge.) Subplex is
-best for unconstrained optimization, but constrained optimization also
-works (both for simple bound constraints via
-.I lb
-and
-.I ub
-as well as nonlinear constraints as described above).
+using the Nelder-Mead simplex algorithm, modified to support bound
+constraints. Nelder-Mead, while popular, is known to occasionally
+fail to converge for some objective functions, so it should be
+used with caution. Anecdotal evidence, on the other hand, suggests
+that it works fairly well for discontinuous objectives. See also
+.B NLOPT_LN_SBPLX
+below.
+.TP
+.B NLOPT_LN_SBPLX
+Perform a local (L) derivative-free (N) optimization, starting at
+.IR x ,
+using an algorithm based on the Subplex algorithm of Rowan et al.,
+which is an improved variant of Nelder-Mead (above). Our
+implementation does not use Rowan's original code, and has some minor
+modifications such as explicit support for bound constraints. (Like
+Nelder-Mead, Subplex often works well in practice, even for
+discontinuous objectives, but there is no rigorous guarantee that it
+will converge.) Nonlinear constraints can be crudely supported
+by returning +Inf when the constraints are violated, as explained above.
.TP
.B NLOPT_LN_PRAXIS
Local (L) derivative-free (N) optimization using the principal-axis
method, based on code by Richard Brent. Designed for unconstrained
-optimization, although bound constraints are supported too (via a
-potentially inefficient method).
+optimization, although bound constraints are supported too (via the
+inefficient method of returning +Inf when the constraints are violated).
.TP
.B NLOPT_LD_LBFGS
Local (L) gradient-based (D) optimization using the limited-memory BFGS
(same without restarting or preconditioning).
.TP
.B NLOPT_GN_CRS2_LM
-Global (G) derivative-free (N) optimization using controlled random
+Global (G) derivative-free (N) optimization using the controlled random
search (CRS2) algorithm of Price, with the "local mutation" (LM)
modification suggested by Kaelo and Ali.
.TP
search uses the derivative/nonderivative algorithm set by
.I nlopt_set_local_search_algorithm
(currently defaulting to
-.I NLOPT_LD_LBFGS
+.I NLOPT_LD_MMA
and
-.I NLOPT_LN_SUBPLEX
+.I NLOPT_LN_COBYLA
for derivative/nonderivative searches, respectively). There are also
two other variants, \fBNLOPT_GD_MLSL\fR and \fBNLOPT_GN_MLSL\fR, which use
pseudo-random numbers (instead of an LDS) as in the original MLSL algorithm.
.B NLOPT_LD_MMA
Local (L) gradient-based (D) optimization using the method of moving
asymptotes (MMA), or rather a refined version of the algorithm as
-published by Svanberg (2002). (NLopt uses an independent free
+published by Svanberg (2002). (NLopt uses an independent free-software/open-source
implementation of Svanberg's algorithm.) The
.B NLOPT_LD_MMA
algorithm supports both bound-constrained and unconstrained optimization,
and also supports an arbitrary number (\fIm\fR) of nonlinear constraints
as described above.
+.TP
+.B NLOPT_LN_COBYLA
+Local (L) derivative-free (N) optimization using the COBYLA algorithm
+of Powell (Constrained Optimization BY Linear Approximations).
+The
+.B NLOPT_LN_COBYLA
+algorithm supports both bound-constrained and unconstrained optimization,
+and also supports an arbitrary number (\fIm\fR) of nonlinear constraints
+as described above.
+.TP
+.B NLOPT_LN_NEWUOA
+Local (L) derivative-free (N) optimization using a variant of the the
+NEWUOA algorithm of Powell, based on successive quadratic
+approximations of the objective function. We have modified the
+algorithm to support bound constraints. The original NEWUOA algorithm
+is also available, as
+.BR NLOPT_LN_NEWUOA ,
+but this algorithm ignores the bound constraints
+.I lb
+and
+.IR ub ,
+and so it should only be used for unconstrained problems.
.SH STOPPING CRITERIA
Multiple stopping criteria for the optimization are supported, as
specified by the following arguments to
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.
-.SH BUGS
-Currently the NLopt library is in pre-alpha stage. Most algorithms
-currently do not support all termination conditions: the only
-termination condition that is consistently supported right now is
-.BR maxeval .
.SH AUTHORS
Written by Steven G. Johnson.
.PP
-Copyright (c) 2007-2008 Massachusetts Institute of Technology.
+Copyright (c) 2007-2014 Massachusetts Institute of Technology.
.SH "SEE ALSO"
nlopt_minimize(3)
~ianmdlvl / nlopt.git / blobdiff