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

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 appr...

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 19; no. 2; pp. 283 - 309
Main Authors: Xu, Huifu, Ye, Jane J.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.06.2011
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Optimization
90C31
SMPEC
90C30
90C46
Coderivative
90C33
C-stationary point
M-stationary point
90C15
Graphical convergence
Sample average approximation
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary: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.
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-010-0160-x