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

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To find the global minimum of a highly non-linear function f(x1, x2, ..., xn) over the domain [0,1]^n, which has numerous local minima, standard minimum search algorithms may be ineffective due to their tendency to get trapped in local minima or the computational burden of calculating high-dimensional Jacobians. Simulated annealing is suggested as a viable alternative, as it can be effectively tuned to navigate the search space and avoid local minima. Other potential methods include genetic algorithms and particle swarm optimization, which may also provide robust solutions for complex optimization problems. The function's evaluation time of about one second necessitates an efficient approach to minimize computational costs. Exploring these advanced optimization techniques could lead to successfully identifying the global minimum.
mikeph
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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
 
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Have you tried simulated annealing? If properly tuned, it can avoid getting stucked into a local minimum.
 

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