Penalized sample average approximation methods for stochastic mathematical programs with complementarity constraints
Penalized sample average approximation methods for stochastic mathematical programs with complementarity constraints
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.
670-694
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Ye, Jane J.
1b5088a1-3dd0-44de-99f6-ace7ea572a44
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Ye, Jane J.
1b5088a1-3dd0-44de-99f6-ace7ea572a44
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), .
(Submitted)
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.
Text
SMPCC-10-Nov-2010.pdf
- Author's Original
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
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Date deposited: 27 Apr 2011 15:29
Last modified: 15 Mar 2024 03:15
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Contributors
Author:
Yongchao Liu
Author:
Huifu Xu
Author:
Jane J. Ye
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