Convergence of a relaxed inertial proximal algorithm for maximally monotone operators

• 成果类型: Article
• 署名作者: Attouch, Hedy; Cabot, Alexandre
• 署名单位: Universite de Montpellier; Universite Bourgogne Europe; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01412-0
• 发表日期: 2020
• 页码: 243-287
• 关键词: WEAK-CONVERGENCE; point algorithm; DYNAMICS

摘要

In a Hilbert spaceHgivenA:H -> 2Ha maximally monotone operator, we study the convergence properties of a general class of relaxed inertial proximal algorithms. This study aims to extend to the case of the general monotone inclusionAxCONTAINS AS MEMBER0the acceleration techniques initially introduced by Nesterov in the case of convex minimization. The relaxed form of the proximal algorithms plays a central role. It comes naturally with the regularization of the operatorAby its Yosida approximation with a variable parameter, a technique recently introduced by Attouch-Peypouquet (Math Program Ser B,2018. 10.1007/s10107-018-1252-x) for a particular class of inertial proximal algorithms. Our study provides an algorithmic version of the convergence results obtained by Attouch-Cabot (J Differ Equ 264:7138-7182,2018) in the case of continuous dynamical systems.