A Tseng type stochastic forward-backward algorithm for monotone inclusions

Abstract

In this paper, we propose a stochastic version of the classical Tseng's forward-backwardforward 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.