A Tseng type stochastic forward-backward algorithm for monotone inclusions

02/20/2022

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by   Van Dung Nguyen, et al.

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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 𝒪(1/n) in expectation for the strong monotone case. Furthermore, we derive 𝒪(1/n) rate convergence of the primal-dual gap for saddle point problems.