A sample average approximation method based on a D-gap function for stochastic variational inequality problems

Abstract

Sample average approximation method is one of the well-behaved methods in the stochastic optimization.This paper presents a sample average approximation method based on a D-gap function for stochastic variational inequality problems.An unconstrained optimization reformulation is proposed for the expected-value formulation of stochastic variational inequality problems based on the D-gap function. An implementable sample average approximation method for the reformulation is established andit is proven that the optimal values and the optimal solutions of the approximation problems converge to their true counterpart with probability one as the sample size increases under some moderate assumptions.Finally, the preliminary numerical results for some test examples are reported, which show that the proposed method is promising.