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

Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints
Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints
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.
sample average approximations, strong law of large numbers, random set-valued mappings, stationary points
0364-765X
648-668
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Meng, Fanwen
7b696c1d-d558-4c77-9540-7e0a5ceaa54e
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Meng, Fanwen
7b696c1d-d558-4c77-9540-7e0a5ceaa54e

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), 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: 79530
URI: http://eprints.soton.ac.uk/id/eprint/79530
ISSN: 0364-765X
PURE UUID: 1631cd40-8f15-4d0c-8c3b-b9b2f77f073d
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

Date deposited: 17 Mar 2010
Last modified: 17 Dec 2019 01:49

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