Efficient unconstrained black box optimization

Abstract For the unconstrained optimization of black box functions, this paper introduces a new randomized algorithm called . In practice, matches quality other state-of-the-art algorithms for finding, in small and large dimensions, local minimizer with reasonable accuracy. Although our theory guarantees only minimizers heuristic techniques turn into an efficient global solver. very thorough numerical experiments, we found most cases either minimizer, or where could not be checked, at least point similar to best competitive solvers. smooth, everywhere defined it is proved that, probability arbitrarily close 1, basic version finds $${{\mathcal {O}}}(n\varepsilon ^{-2})$$ O ( n ? - 2 ) function evaluations whose unknown exact gradient 2-norm below given threshold $$\varepsilon >0$$ > 0 , n dimension. smooth convex case, number improves {O}}}(n\log \varepsilon ^{-1})$$ log 1 (strongly) case n\varepsilon This known recent complexity results reaching slightly different goal, namely expected Numerical show that effective robust comparison solvers on test problems Gould et al. (Comput Optim Appl 60:545–557, 2014) Jamil Yang (Int J Math Model Numer 4:150, 2013) 2–5000 variables.