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Approximating stationary points of stochastic mathematical programs with equilibrium constraints via sample averaging

Approximating stationary points of stochastic mathematical programs with equilibrium constraints via sample averaging
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 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.
smpec, coderivative, graphical convergence, m-stationary point, c-stationary point, sample average approximation
1877-0533
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Ye, Jane J.
1b5088a1-3dd0-44de-99f6-ace7ea572a44
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Ye, Jane J.
1b5088a1-3dd0-44de-99f6-ace7ea572a44

Xu, Huifu and Ye, Jane J. (2010) Approximating stationary points of stochastic mathematical programs with equilibrium constraints via sample averaging. Set-Valued and Variational Analysis. (doi:10.1007/s11228-010-0160-x).

Record type: Article

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.

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Published date: 2010
Additional Information: Online First article
Keywords: smpec, coderivative, graphical convergence, m-stationary point, c-stationary point, sample average approximation
Organisations: Operational Research

Identifiers

Local EPrints ID: 182205
URI: http://eprints.soton.ac.uk/id/eprint/182205
ISSN: 1877-0533
PURE UUID: 7c94fdd6-a007-4f82-b474-c78a168787bc
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

Date deposited: 27 Apr 2011 15:24
Last modified: 15 Mar 2024 03:15

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Contributors

Author: Huifu Xu ORCID iD
Author: Jane J. Ye

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