2-Dimensional Minimization without Derivatives and Ignoring certain Input Parameters on the go -

i have function v depends on 2 variables v1 , v2 , parameter-array p containing 15 parameters. want minimize function v regarding v1 , v2, there no closed expression function, can't build , use derivatives.

the problem following : caluclating value of function need eigenvalues of 2 4x4 matrices (which should symmetric , real concept, eigensolver not real eigenvalues). these eigenvalues calculate eigen package. entries of matrices given v1,v2 , p.

there input sets of these eigenvalues become negative. these input sets want ignore calculation lead complex function value , function allowed have real values.

is there way include this? first attempt nelder-mead-simplex algorithm using gsl-library , way high output value function if 1 of eigenvalues becomes negative, doesn't work.

thanks suggestions.

for nelder-mead simplex, reject new points vertices simplex, unless have desired properties.

your method artificially increase function value forbidden points called penalty or barrier function. might want re-design penalty function.

another optimization method without derivatives simulated annealing method. again, modify method avoid forbidden points.

what mean "doesn't work"? take long? resulting function values high?

depending on function evaluation cost, might approach scan 2d interval, evaluate width x height function values , drill down in tile lowest function values.