Is there someone who could possibly write me the procedure in steps?

Say:

1. Sampling random points from admissible set using [some] multivariate distribution.
2. ….
3. ….
4. ….
5. Result = […].

We are not far from classifying method as a blackbox for now.

Lukas.

That is what I am asking for.

You can see that FindMinimum is called, presumably on random points, although I don't know why there are 2n+1 (there are 11 for me in V11.3, for n = 5):

Trace[
 NMinimize[f, {x, y}, Method -> {"RandomSearch", "SearchPoints" -> 5}],
 _FindMinimum,
 TraceInternal -> True
 ]

Thank you for your answer Daniel!

You gave me very little insight into method. For deeper understanding I would like to know, for example, implicit starting parameters for "PenaltyFunction" (how is chosen, from which space of functions?), "InitialPoints" (how do i find them?). How the radius of hypercube is determined?

I found in help: "The random search algorithm works by generating a population of random starting points and uses a local optimization method from each of the starting points to converge to a local minimum. The best local minimum is chosen to be the solution. " - There are no hypercubes mentioned.

I have no reason to believe that method is not good, but it is hardly defendable for me to use metod that is not properly cited or described.

Thank you for your feedback.