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I need to solve a series of single parameter black-box minimization problem. The underlying cost functions are quite simple. They always have the same shape: a global minimum inside a fixed interval (-15000; 15000).

The constraints are :

  • The function is not differentiable;
  • The function is slow to evaluate.

I can solve these problems using a coarse scan followed by a fine scan. But I need between 30 and 50 evaluations. I'm sure that there is a better way to do it, but I can't find how.

Two examples of these cost functions :

enter image description here enter image description here

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  • $\begingroup$ NOMAD $\endgroup$
    – Kuifje
    Jun 11 at 8:31
  • $\begingroup$ @Kuifje it seems a little too much for this type of problem. I was thinking of something more simple, as I only have 1 parameter to optimize and my function is always convex ... $\endgroup$
    – Kh4zit
    Jun 11 at 11:56
  • $\begingroup$ @Kh4zit, have you faced with an optimization problem? or you are trying to work with a single equation? $\endgroup$
    – A.Omidi
    Jun 11 at 16:44
  • $\begingroup$ Fibonacci search performs slightly better than golden search. $\endgroup$ Jun 27 at 12:22
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Given that your function is apparently unimodal (single local minimum, which is global), you might try golden section search. The first four function evaluations result in about a 40% reduction in the initial interval. Each additional function thereafter again reduces the remaining interval by about 40%.

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  • $\begingroup$ That's exactly the type of solution I was looking for. Thank you ! $\endgroup$
    – Kh4zit
    Jun 12 at 12:14
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I would advise Bayesian Optimization. The benefits imho are that they don’t require a gradient, work for a wide variety of optimization problems and are made for when we are dealing with functions that are hard or slow to evaluate.

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