Convergence analysis of weighted expected residual method for nonlinear stochastic variational inequality problems

A method of convex combined expectations of the least absolute deviation and least squares about the so-called regularized gap function is proposed for solving nonlinear stochastic variational inequality problems (for short, NSVIP). The NSVIP is formulated as a weighted expected residual minimization problem (in short, WERM) in this way. Moreover, we present a discrete approximation of WERM problem by applying the quasi-Monte Carlo method when the sample space is compact, and a compact approximation approach for the case that the sample space is noncompact. The limiting behaviors of optimal solutions of the discrete approximation problem and the compact approximation are also analyzed, respectively.