Solving Optimization Problem: Local Minima Traps & Solutions

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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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