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2014 A Regularization SAA Scheme for a Stochastic Mathematical Program with Complementarity Constraints
Yu-xin Li, Jie Zhang, Zun-quan Xia
J. Appl. Math. 2014: 1-12 (2014). DOI: 10.1155/2014/321010

Abstract

To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC) have drawn much attention in the recent literature. Our concern is the detailed analysis of convergence properties of a regularization sample average approximation (SAA) method for solving a stochastic mathematical program with complementarity constraints (SMPCC). The analysis of this regularization method is carried out in three steps: First, the almost sure convergence of optimal solutions of the regularized SAA problem to that of the true problem is established by the notion of epiconvergence in variational analysis. Second, under MPCC-MFCQ, which is weaker than MPCC-LICQ, we show that any accumulation point of Karash-Kuhn-Tucker points of the regularized SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Finally, some numerical results are reported to show the efficiency of the method proposed.

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Yu-xin Li. Jie Zhang. Zun-quan Xia. "A Regularization SAA Scheme for a Stochastic Mathematical Program with Complementarity Constraints." J. Appl. Math. 2014 1 - 12, 2014. https://doi.org/10.1155/2014/321010

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010597
MathSciNet: MR3170442
Digital Object Identifier: 10.1155/2014/321010

Rights: Copyright © 2014 Hindawi

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