Two-Stage Stochastic Variational Inequalities: Theory, Algorithms and Applications

The stochastic variational inequality (SVI) provides a unified form of optimality conditions of stochastic optimization and stochastic games which have wide applications in science, engineering, economics and finance. In the recent two decades, one-stage SVI has been studied extensively and widely used in modeling equilibrium problems under uncertainty. Moreover, the recently proposed two-stage SVI and multistage SVI can be applied to the case when the decision makers want to make decisions at different stages in a stochastic environment. The two-stage SVI is a foundation of multistage SVI, which is to find a pair of "here-and-now" solution and "wait-and-see" solution. This paper provides a survey of recent developments in analysis, algorithms and applications of the two-stage SVI.