Best way to minimize a function with a vector variable (1x25 vector) ?

Hi,

I am trying to minimize a function that is a function of a 1x25 vector (weights_vector). In other words, I'm trying to find the values in the vector that minimize the function.

The function is defined by

 function weights_correct = Moo(weights_vector)

 corr_matrix = evalin('base', 'corr_matrix');
 tolerance = evalin('base', 'tolerance');
 returns = evalin('base', 'returns');

 weights_correct = weights_vector'*corr_matrix*weights_vector -   tolerance*returns'*weights_vector; 
 end

On this function, I am calling

weights_correct = fminsearch(@Moo, weights_vector);

This iterates until I see the error

"Exiting: Maximum number of function evaluations has been exceeded
         - increase MaxFunEvals option."

Which leads me to believe that I'm not minimizing correctly. What's going on?

[José-Luis]

Optimizing a function with 25 variables is a tall order. Most optimization algorithms will choke with that. If you are using the Nelder Meade algorithm of fminsearch I daresay you are wasting your time. If you have any ideas about the ranges of those variables, I would point you towards: href = ""<http://www.mathworks.com/matlabcentral/fileexchange/8277-fminsearchbnd</a>>

But unless you have very narrow bounds I would recommend against it. You might want to look into some statistical methods, such as Markov Chain Monte Carlo:

href = ""<http://psiexp.ss.uci.edu/research/teachingP205C/205C.pdf</a>>

Cheers!