Stochastic mathematical programs with equilibrium constraints

Stochastic mathematical programs with equilibrium constraints

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Article ID: iaor20052345
Country: Netherlands
Volume: 25
Issue: 4
Start Page Number: 159
End Page Number: 167
Publication Date: Nov 1999
Journal: Operations Research Letters
Authors: ,
Keywords: stochastic processes
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.

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