Adaptive State-Dependent Diffusion for Derivative-Free Optimization  

作　　者：Bjorn Engquist Kui Ren Yunan Yang 

机构地区：[1]Department of Mathematics and the Oden Institute,The University of Texas,Austin,TX 78712,USA [2]Department of Applied Physics and Applied Mathematics,Columbia University,New York,NY10027,USA [3]Department of Mathematics,Cornell University,Ithaca,NY 14853,USA

出　　处：《Communications on Applied Mathematics and Computation》2024年第2期1241-1269,共29页应用数学与计算数学学报（英文）

基　　金：partially supported by the National Science Foundation through grants DMS-2208504(BE),DMS-1913309(KR),DMS-1937254(KR),and DMS-1913129(YY);support from Dr.Max Rossler,the Walter Haefner Foundation,and the ETH Zurich Foundation.

摘　　要：This paper develops and analyzes a stochastic derivative-free optimization strategy.A key feature is the state-dependent adaptive variance.We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples.A striking fact is that convergence is achieved without explicit information of the gradient and even without comparing different objective function values as in established methods such as the simplex method and simulated annealing.It can otherwise be compared to annealing with state-dependent temperature.

关 键 词：Derivative-free optimization Global optimization Adaptive diffusion Stationary distribution Fokker-Planck theory 

分 类 号：O224[理学—运筹学与控制论] TP18[理学—数学]