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Penalized sample average approximation methods for stochastic mathematical programs with complementarity constraints

Record type: Article

This paper considers a one-stage stochastic mathematical program with a complementarity
constraint (SMPCC) where uncertainties appear in both the objective function and the comple-
mentarity constraint, and an optimal decision on both upper and lower level decision variables must
be made before the realization of the uncertainties. A partially exactly penalized sample average
approximation (SAA) scheme is proposed to solve the problem. Asymptotic convergence of optimal
solutions and stationary points of the penalized SAA problem is carried out. It is shown under
some moderate conditions that the statistical estimators obtained from solving the penalized SAA
problems converge almost surely to its true counterpart as the sample size increases.

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Citation

Liu, Yongchao, Xu, Huifu and Ye, Jane J. (2010) Penalized sample average approximation methods for stochastic mathematical programs with complementarity constraints Mathematics of Operations Research, 36, (4), pp. 670-694.

More information

Submitted date: May 2010
Organisations: Operational Research

Identifiers

Local EPrints ID: 182207
URI: http://eprints.soton.ac.uk/id/eprint/182207
ISSN: 0364-765X
PURE UUID: 25a2fdfb-f15d-4b49-9e93-9960de97317b

Catalogue record

Date deposited: 27 Apr 2011 15:29
Last modified: 18 Jul 2017 11:57

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Contributors

Author: Yongchao Liu
Author: Huifu Xu
Author: Jane J. Ye

University divisions


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