- Efficient global unconstrained black box optimization Morteza Kimiaei (kimiaeim83univie.ac.at) Arnold Neumaier (Arnold.Neumaierunivie.ac.at) Abstract: For the unconstrained global optimization of black box functions, this paper presents a new stochastic algorithm called VSBBO. In practice, VSBBO matches the quality of other state-of-the-art algorithms for finding, with reasonable accuracy, a global minimizer in small and large dimensions, or at least in the majority of cases a point as good as competing algorithms. For smooth, everywhere defined functions, it is proved that, with probability arbitrarily close to 1, one finds with $O(n\epsilon^{-2})$ function evaluations a point with gradient 2-norm $\le\epsilon$. In the smooth convex case, this number improves to $O(n\epsilon^{-1})$ and in the smooth strongly convex case to $O(n\log \epsilon^{-1})$. This matches known recent complexity results for reaching a slightly different goal, namely the expected gradient 2-norm $\le\epsilon$. Keywords: Derivative-free optimization, complexity bounds, global optimization, sufficient decrease, line search Category 1: Global Optimization (Stochastic Approaches ) Category 2: Nonlinear Optimization (Unconstrained Optimization ) Citation: Download: [PDF]Entry Submitted: 08/28/2018Entry Accepted: 08/29/2018Entry Last Modified: 03/29/2019Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.