Solving stochastic mathematical programs with complementarity constraints using simulation

Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we report some of the recent progress we had in broadening the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. We first describe the method and the class of stochastic mathematical programs with complementarity constraints that we are interested in solving and then outline a set of sufficient conditions for its almost-sure convergence. We also illustrate an application of the method to solving a toll pricing problem in transportation networks. These developments also make it possible to solve certain stochastic bilevel optimization problems and Stackelberg games, involving expectations or steady-state functions, using simulation.