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Optimization Problem


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I met a problem about finding the optimization of some function. I used the Trust-Region Newton and Quasi-Newton methods for the problem; however, with different initial guesses I sometimes got the local minimums. May I ask how to get out the trap of the local minimums please?

 

I may try the Radom Walk method but it seems not be a good one. Any other ideas please reply! Thanks a lot!

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Genetic algorithms seem to have quite a lot of promise in this area. Last time I took in a seminar about them (2,3 years ago now) there weren't any rigorous proofs that they find the absolute maxima or minima, but an awful lot of anecdotal evidence that they did solving some very difficult problems that the traditional solvers usually can't.

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