Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs

作     者：Howard Heaton Samy Wu Fung Stanley Osher Howard Heaton;Samy Wu Fung;Stanley Osher

作者机构：Typal ResearchTypal LLCLos AngelesUSA Department of Applied Mathematics and StatisticsColorado School of MinesGoldenUSA Department MathematicsUCLALos AngelesUSA 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2024年第6卷第2期

页      面：790-810页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：partially funded by AFOSR MURI FA9550-18-502,ONR N00014-18-1-2527,N00014-18-20-1-2093,N00014-20-1-2787 supported by the NSF Graduate Research Fellowship under Grant No.DGE-1650604 

主　　题：Global optimization Moreau envelope Hamilton-Jacobi Hopf-Lax-Cole-Hopf Proximals Zero-order optimization 

摘      要：Computing tasks may often be posed as optimization *** objective functions for real-world scenarios are often nonconvex and/or ***-of-the-art methods for solving these problems typically only guarantee convergence to local *** work presents Hamilton-Jacobi-based Moreau adaptive descent(HJ-MAD),a zero-order algorithm with guaranteed convergence to global minima,assuming continuity of the objective *** core idea is to compute gradients of the Moreau envelope of the objective(which ispiece-wise convex)with adaptive smoothing *** of the Moreau envelope(i.e.,proximal operators)are approximated via the Hopf-Lax formula for the viscous Hamilton-Jacobi *** numerical examples illustrate global convergence.