Quantitative stability for stochastic tensor variational inequalities

The goal of this article is to investigate a class of stochastic tensor variational inequalities (denoted by STVI), which is a generalization of the stochastic linear variational inequalities (denoted by SLVI) and a subclass of stochastic variational inequalities (denoted by SVI). The quantitative stability of the expected residual minimization (ERM) problem for the STVI is analysed. Firstly, the existence of solutions of the ERM problem and its perturbed problem are considered. Then, the quantitative stability of the ERM problem is derived under suitable probability metrics. Finally, under some suitable assumptions, the rates of convergence of the sample average approximation (SAA) method for the optimal solution sets of the perturbed problems are discussed.