无导数优化求解器附matlab代码.zip

The code was sent by Professor Powell to Zaikun Zhang on December 16th, 2013. The file "email.txt" is the original email. For more information on BOBYQA, you might contact Professor Powell (mjdp@cam.ac.uk). December 16th, 2013 Zaikun Zhang (www.zhangzk.net) Below are the remarks from Professor Powell. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 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. Details of the method of BOBYQA are given in the report "The BOBYQA algorithm for bound constrained optimization without derivatives", which can be reached from the "damtp.cam.ac.uk" home-page on the web, by clicking on "Research at DAMTP", then on "Numerical Analysis" and then on "Reports", the number of the report being 2009/NA06. 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)