Variable Sample-Size Forward-Backward-Forward Algorithm for Two-Stage Stochastic Variational Inequality

In this paper, paper, we propose a novel approach called the variable sample-size forward-backward-forward algorithm to address the two-stage stochastic variational inequality. A key advantage of our algorithm is its requirement for only one projection onto the closed convex set per iteration. By making reasonable assumptions, we demonstrate that the sequence generated by our algorithm converges almost surely. Furthermore, we establish a linear convergence rate for the difference between iterates and solutions, thereby achieving efficient convergence. To validate our proposed method, numerical experiments are conducted to showcase its effectiveness.