NAME

PDL::Opt::Simplex -- Simplex optimization routines

SYNOPSIS

        use PDL::Opt::Simplex;

        ($optimum,$ssize) = simplex($init,$initsize,$minsize,
                        $maxiter,
                        sub {evaluate_func_at($_[0])},
                        sub {display_simplex($_[0])}
                        );

DESCRIPTION

This package implements the commonly used simplex optimization algorithm. The basic idea of the algorithm is that in a N-dimensional search space you choose a simplex of N+1 points which is then moved according to certain rules. The main benefit of the algorithm is that you do not need to calculate the derivatives of your function.

The initial simplex is generated with its centroid at $init, which is assumed to be one-dimensional.

The sub is assumed to understand more than 1 dimensions and threading. Its signature is 'inp(ndims); [ret]out()'.

$ssize gives a very very approximate estimate of how close we might be - it might be miles wrong. It is the euclidean distance between the best and the worst vertices. If it is not very small, the algorithm has not converged.

CAVEATS

Do not use the simplex method if your function has local minima. It will not work. Use genetic algorithms or simulated annealing or conjugate gradient or momentum gradient descent.

They will not work either but they are not guaranteed not to work ;)

SEE ALSO

Ron Shaffer's chemometrics web page and references therein: http://chem1.nrl.navy.mil/~shaffer/chemoweb.html.

Numerical Recipes (bla bla bla).

The demonstration (Examples/Simplex/tsimp.pl).

BUGS

Bad documentation.

AUTHOR

Copyright(C) 1997 Tuomas J. Lukka.