Stochastic quasi-Fejer block-coordinate fixed point iterations with random sweeping II: mean-square and linear convergence
成果类型：
Article
署名作者：
Combettes, Patrick L.; Pesquet, Jean-Christophe
署名单位：
North Carolina State University; Universite Paris Saclay
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-018-1296-y
发表日期：
2019
页码：
433-451
关键词：
摘要：
Combettes and Pesquet (SIAM J Optim 25:1221-1248,2015) investigated the almost sure weak convergence of block-coordinate fixed point algorithms and discussed their applications to nonlinear analysis and optimization. This algorithmic framework features random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and it allows for stochastic errors in the evaluation of the operators. The present paper establishes results on the mean-square and linear convergence of the iterates. Applications to monotone operator splitting and proximal optimization algorithms are presented.