# Stochastic Forward–Backward Splitting for Monotone Inclusions

@article{Rosasco2016StochasticFS, title={Stochastic Forward–Backward Splitting for Monotone Inclusions}, author={Lorenzo Rosasco and Silvia Villa and Bang C{\^o}ng Vu}, journal={Journal of Optimization Theory and Applications}, year={2016}, volume={169}, pages={388-406} }

We propose and analyze the convergence of a novel stochastic algorithm for monotone inclusions that are sum of a maximal monotone operator and a single-valued cocoercive operator. The algorithm we propose is a natural stochastic extension of the classical forward–backward method. We provide a non-asymptotic error analysis in expectation for the strongly monotone case, as well as almost sure convergence under weaker assumptions. For minimization problems, we recover rates matching those obtained…

## 34 Citations

A Tseng type stochastic forward-backward algorithm for monotone inclusions

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The Douglas–Peaceman–Rachford–Varga operator splitting methods are a class of efficient methods for finding a zero of the sum of two maximal monotone operators in a real Hilbert space; however, they…

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