Volume 24, Issue 6
Exponential Convergence of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Omplementarity Constraints

Fan-wen Meng & Hui-fu Xu

DOI:

J. Comp. Math., 24 (2006), pp. 733-748

Published online: 2006-12

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  • 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, G\"{u}rkan and Listes \cite{gur-2}.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.

  • Keywords

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

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@Article{JCM-24-733, author = {}, title = {Exponential Convergence of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Omplementarity Constraints}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {6}, pages = {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, G\"{u}rkan and Listes \cite{gur-2}.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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8787.html} }
TY - JOUR T1 - Exponential Convergence of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Omplementarity Constraints JO - Journal of Computational Mathematics VL - 6 SP - 733 EP - 748 PY - 2006 DA - 2006/12 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8787.html KW - Stochastic mathematical programs with complementarity constraints KW - Sample average approximation KW - Weak stationary points KW - Exponential convergence AB - 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, G\"{u}rkan and Listes \cite{gur-2}.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.
Fan-wen Meng & Hui-fu Xu. (1970). Exponential Convergence of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Omplementarity Constraints. Journal of Computational Mathematics. 24 (6). 733-748. doi:
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