Stochastic Quasi-Fej 'er Block-Coordinate Fixed Point Iterations With\n Random Sweeping II: Mean-Square and Linear Convergence

2017/04/26 by Patrick L. Combettes, Combettes, Patrick L., Jean‐Christophe Pesquet +1 · 1 citation
Computer Science · Mathematics · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.1704.08083

Abstract

Reference [11] investigated the almost sure weak convergence of\nblock-coordinate fixed point algorithms and discussed their applications to\nnonlinear analysis and optimization. This algorithmic framework features random\nsweeping rules to select arbitrarily the blocks of variables that are activated\nover the course of the iterations and it allows for stochastic errors in the\nevaluation of the operators. The present paper establishes results on the\nmean-square and linear convergence of the iterates. Applications to monotone\noperator splitting and proximal optimization algorithms are presented.\n

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• Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature

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