Stochastic golden ratio algorithm to non-convex stochastic mixed variational inequality problem

In [Grad and Lara, J. Optim. Theory Appl. 190(2), 565–580 (2021)], the authors proposed a golden ratio algorithm for solving the deterministic mixed variational inequality problem with prox-convex function. In this paper, we study a new class of stochastic mixed variational inequality problems with the expectation of a prox-convex stochastic function and present a stochastic golden ratio algorithm for solving the proposed problem. The convergence and the convergence rate of our algorithm are shown under some simple and necessary conditions. Finally, we present some numerical examples to illustrate the efficiency of the proposed algorithm.