Regularized Sample Average Approximation Approach for Two-Stage Stochastic Variational Inequalities

Sample average approximation (SAA) approach for two-stage stochastic variational inequalities (SVIs) with continuous probability distributions, where the second-stage problems have multiple solutions, may not promise convergence assertions as the sample size tends to infinity. In this paper, a regularized SAA approach is proposed to numerically solve a class of two-stage SVIs with continuous probability distributions, where the second-stage problems are monotone and allowed to have multiple solutions. We first give some structural properties. After that, the convergence analysis of the regularized SAA approach for two-stage SVIs is investigated as the regularization parameter tends to zero and the sample size tends to infinity. Finally, we employ the progressive hedging algorithm to report some numerical results.