Exponential Convergence of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Complementarity Constraints

Exponential Convergence of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Complementarity Constraints

Year:    2006

Author:    Fan-wen Meng, Hui-fu Xu

Journal of Computational Mathematics, Vol. 24 (2006), Iss. 6 : pp. 733–748

Abstract

In this paper, we propose a Sample Average Approximation (SAA) method for a class of Stochastic Mathematical Programs with Complementarity Constraints (SMPCC) recently considered by Birbil, Gürkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes' regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2006-JCM-8787

Journal of Computational Mathematics, Vol. 24 (2006), Iss. 6 : pp. 733–748

Published online:    2006-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Stochastic mathematical programs with complementarity constraints Sample average approximation Weak stationary points Exponential convergence.

Author Details

Fan-wen Meng

Hui-fu Xu