Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations With Random Sweeping II: Mean-Square and Linear Convergence

2017/04/26 by Patrick L. Combettes, Combettes, Patrick L., Jean‐Christophe Pesquet +2 · 2 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Fixed Point Theorems Analysis #Optimization and Variational Analysis #math.OC

paper · pdf · doi:10.48550/arxiv.1704.08083

arxiv created 2018/04/16 · arxiv updated 2018/04/17

Abstract

Reference [11] 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.

Cited by

• Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
• A Geometric Framework for Stochastic Iterations

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