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Stochastic mathematical programs with equilibrium constraints. (English) Zbl 0937.90076
Summary: 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.

MSC:
90C15 Stochastic programming
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
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