An inexact algorithm for stochastic variational inequalities

Abstract

We present a new Progressive Hedging Algorithm to solve Stochastic Variational Inequalities in the formulation introduced by Rockafellar and Wets in 2017, allowing the generated subproblems to be approximately solved with an implementable tolerance condition. Our scheme is based on Hybrid Inexact Proximal Point methods and generalizes the exact algorithm developed by Rockafellar and Sun in 2019, providing stronger convergence results. We also show some numerical experiments in two-stage Nash games.