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Section: New Results

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

Participants: Jean-Christophe Pesquet (in collaboration with Patrick L. Combettes, North Caroline State University)

In one of our previous works, we investigated the almost sure weak convergence of a block-coordinate fixed point algorithm and discussed its application to nonlinear analysis and optimization. This algorithm 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.