--- /dev/null
+===========================================================================
+On 8/13/09 added the paper on BOBYQA
+===========================================================================
+
+For simplicity, the Makefi;e has been replaced by a one-line compile
+script "comp" which needs to be adjusted if the compiler name is not
+f77. All Fortran files are in bobyla.f. Compiling and running bobyqa
+should produce results similar to those in RESULTS.
+ Hans Mittelmann, Jan 2009
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+ The Fortran version of BOBYQA is attached. Its purpose is to seek
+the least value of a function F of several variables, when derivatives
+are not available, where F is specified by the user through a subroutine
+called CALFUN. The name BOBYQA denotes Bound Approximation BY Quadratic
+Approximation, the constraints being lower and upper bounds on every
+variable, which can be set to huge values for unconstrained variables.
+The algorithm is intended to change the variables to values that are close
+to a local minimum of F. The user, however, should assume responsibility for
+finding out if the calculations are satisfactory, by considering carefully
+the values of F that occur. The BOBYQA software has been developed from the
+method of the paper "The NEWUOA software for unconstrained minimization
+without derivatives", in Large-Scale Nonlinear Optimization, editors G. Di
+Pillo and M. Roma, Springer (2006), pages 255-297. A report that describes
+the details of the development is going to be written soon.
+
+ The attachments in sequence are a suitable Makefile, followed by a main
+program and a CALFUN routine for the "Invdist2" problem, in order to provide
+an example for testing. Then BOBYQA and its six auxiliary routines, namely
+BOBYQB, ALTMOV, PRELIM, RESCUE, TRSBOX and UPDATE, are given. Finally, the
+computed output that the author obtained for the Invdist2 problems is listed.
+
+ In addition to providing CALFUN, an initial vector of variables and
+the lower and upper bounds, the user has to set the values of the parameters
+RHOBEG, RHOEND and NPT. After scaling the individual variables if necessary,
+so that the magnitudes of their expected changes are similar, RHOBEG is the
+initial steplength for changes to the variables, a reasonable choice being
+the mesh size of a coarse grid search. Further, RHOEND should be suitable for
+a search on a very fine grid. Typically, the software calculates a vector
+of variables that is within distance 10*RHOEND of a local minimum. Another
+consideration is that every trial vector of variables is forced to satisfy
+the lower and upper bounds, but there has to be room to make a search in all
+directions. Therefore an error return occurs if the difference between the
+bounds on any variable is less than 2*RHOBEG. The parameter NPT specifies
+the number of interpolation conditions on each quadratic model, the value
+NPT=2*N+1 being recommended for a start, where N is the number of variables.
+It is often worthwhile to try other choices too, but much larger values tend
+to be inefficient, because the amount of routine work of each iteration is
+of magnitude NPT**2, and because the achievement of adequate accuracy in some
+matrix calculations becomes more difficult. Some excellent numerical results
+have been found in the case NPT=N+6 even with more than 100 variables.
+
+ The way of calling BOBYQA should be clear from the Invdist2 examples
+and from the comments near the beginning of SUBROUTINE BOBYQA. There are no
+restrictions on or charges for the use of the software. I hope that the time
+and effort I have spent on developing the package will be helpful to much
+research and to many applications.
+
+January 5th, 2009 M.J.D. Powell (mjdp@cam.ac.uk)
+
~ianmdlvl / nlopt.git / commitdiff