Best optimization algorithm for minimization of a chi-square function with about 20 parameters

Dear all,

I am faced to a minimization problem of a chi-square function with about 20 parameters. I would like to have advice on what is the best algorithm to solve the problem. I have tried fmisearch, which is ok if I run it twice. I can have access to the following toolbox:

• Global Optimization Toolbox
• Optimization Toolbox

Thanks for your help.

Answer 1

[Alan Weiss]

Well, if your objective function is smooth, you might just want to use MultiStart along with fmincon or fminunc to minimize the function. I am assuming that there are multiple local minima and that you want a global solution. Or, for a local solution or to try things out, you could just try fmincon or fminunc starting from an appropriate initial point.

If your objective function is not smooth, then I suggest that you try patternsearch.

These suggestions are codified in the doc: for smooth functions, Optimization Decision Table, and for nonsmooth functions, Table for Choosing a Solver. By the way, there is an unfortunate typo in the latter page; the correct way to get initial points in bounded regions is to take

x0 = lb + rand(size(lb)).*(ub - lb);

Alan Weiss

MATLAB mathematical toolbox documentation

[alexia gorecki]

Thanks a lot. I'll try what you've suggested.