Stochastic variational inequalities and applications

Stochastic variational inequalities provide a general framework to study nonlinear optimization and Nash-type equilibrium problems with uncertain model data. An optimization problem that optimizes the expected value of a random function can be written into a stochastic variational inequality, if the objective function is differentiable. An equilibrium problem in which each player optimizes his/her expected profit can also be formulated as a stochastic variational inequality under mild conditions.

Solving a stochastic variational inequality often requires replacing the exact values of expectations by sample averages, resulting in the sample average approximation (SAA) problems. By studying the convergence of solutions to the SAA problems, we have developed methods to compute confidence regions and confidence intervals for the true solution based on an SAA solution. This talk will give an overview of these methods, and discuss applications in areas such as energy markets, portfolio selection, and traffic equilibria.