Find global minimum of f(x1,x2, xn), with many local minima

[mikeph]

Hi

I have some function f = f(x1,x2,...xn) over some domain [0,1]^n, and I'd like to find the global minimum. The function is *highly* non-linear and takes about 1 second to evaluate. I know it's positive because it's the sum of squares of about 1,000,000 arguments, each of which pretty much depends (non-linearly) on every single argument x1,x2...xn., where n ≈ 50; As a result I expect there to be a very large number of local minima.

Can anyone suggest a good approach to this problem? Standard minimum search algorithms get lost in a local minima or take forever calculating 50-D Jacobians.

Any suggestions?
Thanks

 

[csopi]

Have you tried simulated annealing? If properly tuned, it can avoid getting stucked into a local minimum.