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Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints

Xu, Huifu and Meng, Fanwen (2007) Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints Mathematics of Operations Research, 32, (3), pp. 648-668. (doi:10.1287/moor.1070.0260).

Record type: Article

Abstract

In this paper we discuss the sample average approximation (SAA) method for a class of stochastic programs with nonsmooth equality constraints. We derive a uniform Strong Law of Large Numbers for random compact set-valued mappings and use it to investigate the convergence of Karush-Kuhn-Tucker points of SAA programs as the sample size increases. We also study the exponential convergence of global minimizers of the SAA problems to their counterparts of the true problem. The convergence analysis is extended to a smoothed SAA program. Finally, we apply the established results to a class of stochastic mathematical programs with complementarity constraints and report some preliminary numerical test results.

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More information

Published date: August 2007
Keywords: sample average approximations, strong law of large numbers, random set-valued mappings, stationary points
Organisations: Operational Research

Identifiers

Local EPrints ID: 48358
URI: http://eprints.soton.ac.uk/id/eprint/48358
ISSN: 0364-765X
PURE UUID: f57e9915-3c5d-4cb7-949e-c64c8f4f372a

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Date deposited: 17 Sep 2007
Last modified: 17 Jul 2017 15:00

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Contributors

Author: Huifu Xu
Author: Fanwen Meng

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