Convergence rate of inertial Forward-Backward algorithm beyond Nesterov's rule

• 成果类型: Article
• 署名作者: Apidopoulos, Vassilis; Aujol, Jean-Francois; Dossal, Charles
• 署名单位: Universite de Bordeaux; 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/s10107-018-1350-9
• 发表日期: 2020
• 页码: 137-156
• 关键词: inexact

摘要

In this paper we study the convergence of an Inertial Forward-Backward algorithm, with a particular choice of an over-relaxation term. In particular we show that for a sequence of over-relaxation parameters, that do not satisfy Nesterov's rule, one can still expect some relatively fast convergence properties for the objective function. In addition we complement this work by studying the convergence of the algorithm in the case where the proximal operator is inexactly computed with the presence of some errors and we give sufficient conditions over these errors in order to obtain some convergence properties for the objective function.