An inexact algorithm for stochastic variational inequalities

TL;DR

This paper introduces a new inexact Progressive Hedging Algorithm for stochastic variational inequalities, allowing approximate subproblem solutions and providing improved convergence results, demonstrated through numerical experiments in Nash games.

Contribution

It generalizes existing algorithms by incorporating inexact solutions with stronger convergence guarantees for stochastic variational inequalities.

Findings

Algorithm converges under inexact subproblem solutions

Numerical experiments validate effectiveness in Nash games

Provides a practical approach for large-scale stochastic problems

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 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.