# Principle of RandomSearch method in NMinimize?

GROUPS:
 Hello everyone, I am using NMinimize procedure with RandomSearch method explicitly chosen for optimization of a non-convex 6 dimensional problem. Those 6 variables are non-negative and they sum up to one.Can someone explain me how does RandomSearch method in Wolfram Language environment work? It is unclear from http://reference.wolfram.com/language/tutorial/ConstrainedOptimizationGlobalNumerical.htmlFor example: "... generating a population of random starting points…“ - how admissible solutions are obtained? From which (multivariate) distribution we are sampling from? A similar question may be asked for remaining 3 methods, "NelderMead", "DifferentialEvolution", and "SimulatedAnnealing".The method seems to be different from method described at en.wikipedia.org/wiki/Random_search where hypercubes are mentioned. Am I right?Thank you for your answers!
16 days ago
5 Replies
 If I remember correctly hypercubes are used for this. Except if there are explicit linear inequality constraints, linear programming is used to find viable points in "random" directions. For equality constraints I believe variables are solved for in terms of others, and inequalities are changed accordingly.
16 days ago
 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.
 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 ]