Can anyone comment on the most suitable approach for the following optimization problem:
We are given finite bounds for a set of $n$ real-valued parameters of an unknown deterministic function. The function is a black-box and we cannot assume convexity. It's execution cannot be parallelised, hence we obtain 1 output value at a time and can re-evaluate our strategy after each step. We are interested to find a global minimum of the function.
(so far this problem can be solved using one of the many optimization heuristics mentioned here)
I wonder if the choice of algorithms becomes more constrained if we specify upfront an upper bound on the number of steps $s$ we can perform (i.e. we limit the number of evaluations of our expensive black-box function).
Was any of the known global optimization heuristics shown to dominate the others for specific values of $n$ and $s$ (and perhaps also with regard to differing tightness of bounds on $n$)?
It seems that if we can incorporate priors on the search space, we can use a Gaussian process to model the minimization function as shown in this paper. I wonder if there are strong thoughts for, or against this approach by anyone who has successfully solved such problems?