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arXiv · 2202.09759

A Tseng type stochastic forward-backward algorithm for monotone inclusions

Van Dung Nguyen·Nguyen The Vinh
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Abstract

In this paper, we propose a stochastic version of the classical Tseng's forward-backward-forward method with inertial term for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued monotone operator in real Hilbert spaces. We obtain the almost sure convergence for the general case and the rate $\mathcal{O}(1/n)$ in expectation for the strong monotone case. Furthermore, we derive $\mathcal{O}(1/n)$ rate convergence of the primal-dual gap for saddle point problems.

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Van Dung Nguyen, Nguyen The Vinh. 2022-02-20. A Tseng type stochastic forward-backward algorithm for monotone inclusions. https://arxiv.org/abs/2202.09759

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