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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
Exponential convergence of sample average approximation methods for a class of stochastic mathematical programs with complementarity constraints
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. 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.
0254-9409
733-748
Meng, F.
cd08ca32-399c-4612-a697-29e68f45f2fc
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Meng, F.
cd08ca32-399c-4612-a697-29e68f45f2fc
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

Meng, F. and Xu, Huifu (2006) Exponential convergence of sample average approximation methods for a class of stochastic mathematical programs with complementarity constraints. Journal of Computational Mathematics, 24 (6), 733-748.

Record type: Article

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. 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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Published date: 2006
Organisations: Operational Research

Identifiers

Local EPrints ID: 79541
URI: http://eprints.soton.ac.uk/id/eprint/79541
ISSN: 0254-9409
PURE UUID: cc977796-f349-439e-96d4-4cf202800ab6
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

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Date deposited: 17 Mar 2010
Last modified: 07 Aug 2019 00:44

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