Journal of Applied Mathematics

A Regularization SAA Scheme for a Stochastic Mathematical Program with Complementarity Constraints

Yu-xin Li, Jie Zhang, and Zun-quan Xia

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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.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 321010, 12 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305520

Digital Object Identifier
doi:10.1155/2014/321010

Mathematical Reviews number (MathSciNet)
MR3170442

Zentralblatt MATH identifier
07010597

Citation

Li, Yu-xin; Zhang, Jie; Xia, Zun-quan. A Regularization SAA Scheme for a Stochastic Mathematical Program with Complementarity Constraints. J. Appl. Math. 2014 (2014), Article ID 321010, 12 pages. doi:10.1155/2014/321010. https://projecteuclid.org/euclid.jam/1425305520


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