Inertial stochastic reflected forward backward method with applications to traffic network problems

This paper introduces a new inertial stochastic reflected-forward-backward splitting method aimed at addressing monotone inclusion problems, specifically involving a maximal monotone set-valued operator and a single-valued Lipschitz continuous and monotone operator within a real separable Hilbert space. Distinct from many existing inertial splitting approaches, this algorithm uniquely depends on one unbiased estimate of the monotone Lipschitz continuous operator and a single backward computation of the maximal monotone operator per iteration. We establish a convergence rate of in expectation for a case of strong monotonicity, and almost sure convergence for a general monotone scenario. Furthermore, we examine its application to traffic flow networks.