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Approximating Stationary Points of Stochastic Mathematical Programs with Equilibrium Constraints via Sample Averaging

Huifu Xu (h.xu***at***soton.ac.uk)
Jane J. Ye (janeye***at***uvic.ca)

Abstract: We investigate sample average approximation of a general class of one-stage stochastic mathematical programs with equilibrium constraints. By using graphical convergence of unbounded set-valued mappings, we demonstrate almost sure convergence of a sequence of stationary points of sample average approximation problems to their true counterparts as the sample size increases. In particular we show the convergence of M(Mordukhovich)-stationary point and C(Clarke)-stationary point of the sample average approximation problem to those of the true problem. The research complements the existing work in the literature by considering a general constraint to be represented by a stochastic generalized equation and exploiting graphical convergence of coderivative mappings.

Keywords: SMPEC, coderivative, graphical convergence, M-stationary point, C-stationary point, sample average approximation

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Stochastic Programming

Category 3: Complementarity and Variational Inequalities


Download: [Postscript][PDF]

Entry Submitted: 08/11/2010
Entry Accepted: 08/11/2010
Entry Last Modified: 08/25/2010

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