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I have a bounded non-convex function in 10-dimensional space. The function is quasi-smooth, you can imagine a histogram, here is an illustration, it just shows the idea and not related to my particular function:

enter image description here

The function value is obtained by time consuming simulation (it takes about 10 seconds). Obviously if I want compute gradients, I need to approximate them by difference quotients. If you need more details about the function, I might be able to say more.

I have read the article of L.M. Rios and N.V. Sahinidis, Derivative-free optimization: A review of algorithms and comparison of software implementations

So I've tried all of TOMLAB solvers, proposed in article and also MCS method, also mentioned in the article as one of the best. But neither of them could not overperform simple Brent method accompanied by hand picked initial guess (well, I hardly believe I can produce such great guesses).

I've heard about surrogate modeling, is it worth trying?

So which other global optimization methods should I consider?

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  • $\begingroup$ May be genetic algorithm or simulated annealing ? $\endgroup$
    – forecaster
    Commented Oct 11, 2014 at 2:49
  • $\begingroup$ @forecaster yeah, I've tried simulated annealing as well, but in vain. $\endgroup$
    – JohnnyBGoode
    Commented Oct 11, 2014 at 12:30
  • $\begingroup$ any chance you can post your function ?, you could also try a hybrid global/local optimizer example: GA-nedler mead or Simulated annealing - neadler mead method ? $\endgroup$
    – forecaster
    Commented Oct 12, 2014 at 2:43
  • $\begingroup$ @forecaster no, not a chance, function value is a result of simulation $\endgroup$
    – JohnnyBGoode
    Commented Oct 12, 2014 at 10:35

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