On the existence of solutions to stochastic mathematical programs with equilibrium constraints

We generalize Stochastic Mathematical Programs with Equilibrium Constraints (SMPEC) introduced by Patriksson and Wynter [Operations Research Letters, Vol. 25, pp. 159–167, 1999] to allow joint upper-level constraints, and to change continuity assumptions w.r.t. uncertainty parameter assumed before by measurability assumptions. For this problem, we prove the measurability of a lower-level mapping and the existence of solutions. We also discuss algorithmic aspects of the problem, in particular the construction of an inexact penalty function for the SMPEC problem, and touch upon a question of distribution sensitivity. Applications to structural topology optimization and other fields are mentioned.