Stochastic mathematical programs with equilibrium constraints

Authors:
Michael Patriksson;Laura Wynter
Affiliations:
Department of Mathematics, Chalmers University of Technology, Gothenburg, Sweden;PRISM, Computer Science Department, Université de Versailles, Versailles, France
Venue:
Operations Research Letters
Year:
1999

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Abstract

We introduce stochastic mathematical programs with equilibrium constraints (SMPEC), which generalize MPEC models by explicitly incorporating possible uncertainties in the problem data to obtain robust solutions to hierarchical problems. For this problem, we establish results on the existence of solutions, and on the convexity and directional differentiability of the implicit upper-level objective function, both for continuously and discretely distributed probability distributions. In so doing, we establish links between SMPEC models and two-stage stochastic programs with recourse. We also discuss basic parallel iterative algorithms for discretely distributed SMPEC problems.