jdistlib.math.opt

Class Bobyqa

java.lang.Object

jdistlib.math.opt.MultivariateOptimization

jdistlib.math.opt.Bobyqa

public class Bobyqa
extends MultivariateOptimization

Translation of the infamous Bobyqa algorithm by Michael J. D. Powell. Original Fortran code can be found here. Paper is here

Constructor Summary

Constructors

Constructor and Description
Bobyqa()

Method Summary

Modifier and Type	Method and Description
static OptimizationResult	bobyqa(double[] x, double[] xl, double[] xu, MultivariableFunction calfun, int npt, double rhobeg, double rhoend, int maxfun, boolean isMinimize) This subroutine seeks the least value of a function of many variables, by applying a trust region method that forms quadratic models by interpolation.
static void	main(java.lang.String[] args)
OptimizationResult	optimize(OptimizationConfig cfg)

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Bobyqa

public Bobyqa()

Method Detail

optimize

public OptimizationResult optimize(OptimizationConfig cfg)

Specified by:

optimize in class MultivariateOptimization

bobyqa

public static final OptimizationResult bobyqa(double[] x,
                                              double[] xl,
                                              double[] xu,
                                              MultivariableFunction calfun,
                                              int npt,
                                              double rhobeg,
                                              double rhoend,
                                              int maxfun,
                                              boolean isMinimize)

 This subroutine seeks the least value of a function of many variables,
 by applying a trust region method that forms quadratic models by
 interpolation. There is usually some freedom in the interpolation
 conditions, which is taken up by minimizing the Frobenius norm of
 the change to the second derivative of the model, beginning with the
 zero matrix. The values of the variables are constrained by upper and
 lower bounds. The arguments of the subroutine are as follows.
 
 N must be set to the number of variables and must be at least two.
 NPT is the number of interpolation conditions. Its value must be in
   the interval [N+2,(N+1)(N+2)/2]. Choices that exceed 2*N+1 are not
   recommended.
 Initial values of the variables must be set in X(1),X(2),...,X(N). They
   will be changed to the values that give the least calculated F.
 For I=1,2,...,N, XL(I) and XU(I) must provide the lower and upper
   bounds, respectively, on X(I). The construction of quadratic models
   requires XL(I) to be strictly less than XU(I) for each I. Further,
   the contribution to a model from changes to the I-th variable is
   damaged severely by rounding errors if XU(I)-XL(I) is too small.
 RHOBEG and RHOEND must be set to the initial and final values of a trust
   region radius, so both must be positive with RHOEND no greater than
   RHOBEG. Typically, RHOBEG should be about one tenth of the greatest
   expected change to a variable, while RHOEND should indicate the
   accuracy that is required in the final values of the variables. An
   error return occurs if any of the differences XU(I)-XL(I), I=1,...,N,
   is less than 2*RHOBEG.
 The value of IPRINT should be set to 0, 1, 2 or 3, which controls the
   amount of printing. Specifically, there is no output if IPRINT=0 and
   there is output only at the return if IPRINT=1. Otherwise, each new
   value of RHO is printed, with the best vector of variables so far and
   the corresponding value of the objective function. Further, each new
   value of F with its variables are output if IPRINT=3.
 MAXFUN must be set to an upper bound on the number of calls of CALFUN.
 The array W will be used for working space. Its length must be at least
   (NPT+5)*(NPT+N)+3*N*(N+5)/2.
   
 DOUBLE PRECISION FUNCTION CALFUN (N,X,IP) has to be provided by
 the user. It returns the value of the objective function for
 the current values of the variables X(1),X(2),...,X(N), which are
 generated automatically in a way that satisfies the bounds given
 in XL and XU.
 
 Return if the value of NPT is unacceptable.
 

RJ's note: Storage bound [3.5*n^2 + 23.5*n + 14, (n^4 + 35*n^2)/4 + 2*n^3 + 24*n + 6]

Parameters:

x - Initial estimate

xl - Lower estimate

xu - Upper estimate

calfun - Function to optimize

npt - Number of interpolation points

rhobeg - Initial trust region radius

rhoend - Final trust region radius

maxfun - Maximum number of calls to calfun

isMinimize - true if goal is to find the global minimum

main

public static void main(java.lang.String[] args)