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


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), 670-694. (Submitted).

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Description/Abstract

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.

Item Type: Article
ISSNs:

Subjects: Q Science > QA Mathematics > QA76 Computer software
Divisions: University Structure - Pre August 2011 > School of Mathematics > Operational Research
Faculty of Social and Human Sciences > Mathematical Sciences > Operational Research
ePrint ID: 182207
Date Deposited: 27 Apr 2011 15:29
Last Modified: 27 Mar 2014 19:35
URI: http://eprints.soton.ac.uk/id/eprint/182207

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