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A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints

A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints
A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints
We investigate a class of two stage stochastic programs where the second stage problem is subject to nonsmooth equality constraints parameterized by the first stage variant and a random vector. We consider the case when the parametric equality constraints have more than one solution. A regularization method is proposed to deal with the multiple solution problem, and a sample average approximation method is proposed to solve the regularized problem. We then investigate the convergence of stationary points of the regularized sample average approximation programs as the sample size increases. The established results are applied to stochastic mathematical programs with $P_0$-variational inequality constraints. Preliminary numerical results are reported.
1052-6234
891-919
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) A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints. SIAM Journal on Optimization, 17 (3), 891-919. (doi:10.1137/050638242).

Record type: Article

Abstract

We investigate a class of two stage stochastic programs where the second stage problem is subject to nonsmooth equality constraints parameterized by the first stage variant and a random vector. We consider the case when the parametric equality constraints have more than one solution. A regularization method is proposed to deal with the multiple solution problem, and a sample average approximation method is proposed to solve the regularized problem. We then investigate the convergence of stationary points of the regularized sample average approximation programs as the sample size increases. The established results are applied to stochastic mathematical programs with $P_0$-variational inequality constraints. Preliminary numerical results are reported.

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More information

Published date: 2006
Organisations: Operational Research

Identifiers

Local EPrints ID: 79542
URI: http://eprints.soton.ac.uk/id/eprint/79542
ISSN: 1052-6234
PURE UUID: 563668b0-72f9-4366-82fc-fccb26f85db5
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

Date deposited: 17 Mar 2010
Last modified: 12 Nov 2019 01:49

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