Stability analysis of two stage stochastic mathematical
programs with complementarity constraints via NLP-regularization
Stability analysis of two stage stochastic mathematical
programs with complementarity constraints via NLP-regularization
This paper presents numerical approximation schemes for a two stage stochastic programming problem where the second stage problem has a general nonlinear complementarity constraint: first, the complementarity constraint is approximated by a parameterized system of inequalities with a well-known regularization approach (SIOPT, Vol.11, 918-936) in deterministic mathematical programs with equilibrium constraints; the distribution of the random variables of the regularized two stage stochastic program is then approximated by a sequence of probability measures. By treating the approximation problems as a perturbation of the original (true) problem, we carry out a detailed stability analysis of the approximated problems including continuity and local Lipschitz continuity of optimal value functions, and outer semicontinuity and continuity of the set of optimal solutions and stationary points. A particular focus is given to the case when the probability distribution is approximated by the empirical probability measure which is known as sample average approximation.
smpcc, nlp-regularization, mpec-mfcq, stability analysis, sample average approximation
669-705
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Lin, Gui-Hua
9c0a405f-5e2a-4d01-a6eb-a2401295ce2b
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Lin, Gui-Hua
9c0a405f-5e2a-4d01-a6eb-a2401295ce2b
Liu, Yongchao, Xu, Huifu and Lin, Gui-Hua
(2010)
Stability analysis of two stage stochastic mathematical
programs with complementarity constraints via NLP-regularization.
SIAM Journal on Optimization, 21 (3), .
(In Press)
Abstract
This paper presents numerical approximation schemes for a two stage stochastic programming problem where the second stage problem has a general nonlinear complementarity constraint: first, the complementarity constraint is approximated by a parameterized system of inequalities with a well-known regularization approach (SIOPT, Vol.11, 918-936) in deterministic mathematical programs with equilibrium constraints; the distribution of the random variables of the regularized two stage stochastic program is then approximated by a sequence of probability measures. By treating the approximation problems as a perturbation of the original (true) problem, we carry out a detailed stability analysis of the approximated problems including continuity and local Lipschitz continuity of optimal value functions, and outer semicontinuity and continuity of the set of optimal solutions and stationary points. A particular focus is given to the case when the probability distribution is approximated by the empirical probability measure which is known as sample average approximation.
Text
SMPEC-Liu-Xu-Lin.pdf
- Accepted Manuscript
More information
Accepted/In Press date: 11 February 2010
Keywords:
smpcc, nlp-regularization, mpec-mfcq, stability analysis, sample average approximation
Organisations:
Operational Research
Identifiers
Local EPrints ID: 156457
URI: http://eprints.soton.ac.uk/id/eprint/156457
ISSN: 1052-6234
PURE UUID: 273ac6df-95fd-4117-a3d5-8e2646087470
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Date deposited: 01 Jun 2010 09:51
Last modified: 14 Mar 2024 02:47
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Contributors
Author:
Yongchao Liu
Author:
Huifu Xu
Author:
Gui-Hua Lin
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