Global optimization

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Assume that I want to find the global minimum of a non-linear, non-convex, multidimensional function subject to several restrictions.

Could you recommend me any deterministic strategy which can generally find an acceptable solution in a reasonable time-frame (say less than 1 hour)? Or should I go with the heuristic / stochastic route?


Ok, I will slightly rephrase the question:

If you had to find the global optimum of a multidimensional non-convex function, are there any type of problem/structure where deterministic strategies will be preferred to other stochastic/heuristic methods like simulated annealing or a genetic algorithm.