We consider the global optimization problem for d-variate Lipschitz functions which, in a certain sense, do not increase too slowly in a neighborhood of the global minimizer(s). On these functions, we apply optimization algorithms which use only function values. We propose two adaptive deterministic methods. The first one applies in a situation when the Lipschitz constant L is known. The second one applies if L is unknown. We show that for an optimal method, adaptiveness is necessary and that randomization (Monte Carlo) yields no further advantage. Both algorithms presented have the optimal rate of convergence. © 2005 Elsevier Inc. All rights reserved.
Horn, M. (2006). Optimal algorithms for global optimization in case of unknown Lipschitz constant. Journal of Complexity, 22(1 SPEC. ISS.), 50–70. https://doi.org/10.1016/j.jco.2005.06.006