Regularizations for Stochastic Linear Variational Inequalities
This paper applies the MoreauYosida regularization to a convex expected residual minimization (ERM) formulation for a class of stochastic linear variational inequalities. To have the convexity of the corresponding sample average approximation (SAA) problem, we adopt the Tikhonov regularization. We show that any cluster point of minimizers of the Tikhonov regularization for the SAA problem is a minimizer of the ERM formulation with probability one as the sample size goes to infinity and the Tikhonov regularization parameter goes to zero. Moreover, we prove that the minimizer is the least \(l_2\)-norm solution of the ERM formulation. We also prove the semismoothness of the gradient of the MoreauYosida and Tikhonov regularizations for the SAA problem.
expected residual minimization sample average approximations semismooth stochastic variational inequality epi-convergence 90c33 90c15