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## Section: New Results

### Stochastic quasi-Fejér block-coordinate fixed point iterations with random sweeping: Mean-square and linear convergence

Participant: Jean-Christophe Pesquet (Collaboration: Patrick Louis Combettes, North Carolina University, USA)

In our previous work, we 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 paper [14] establishes results on the mean-square and linear convergence of the iterates. Applications to monotone operator splitting and proximal optimization algorithms are presented.