Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems

Abstract

This paper considers the expected residual minimization (ERM) method proposed by Luo and Lin (J. Optim. Theory Appl. 140:103-116, 2009) for a class of stochastic variational inequality problems. Different from the work mentioned above, the function involved is assumed to be nonlinear in this paper. We first consider a quasi-Monte Carlo method for the case where the underlying sample space is compact and show that the ERM method is convergent under very mild conditions. Then, we suggest a compact approximation approach for the case where the sample space is noncompact.