Stability analysis of two stage stochastic mathematical programs with complementarity constraints via NLP-regularization
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), 669-705. (In Press).
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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.
|Keywords:||smpcc, nlp-regularization, mpec-mfcq, stability analysis, sample average approximation|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Operational Research
Faculty of Social and Human Sciences > Mathematical Sciences > Operational Research
|Date Deposited:||01 Jun 2010 09:51|
|Last Modified:||08 Jun 2012 12:51|
|Contributors:||Liu, Yongchao (Author)
Xu, Huifu (Author)
Lin, Gui-Hua (Author)
|Date:||11 February 2010|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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