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Stochastic mathematical programs with probabilistic complementarity constraints: SAA and distributionally robust approaches
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2021 (English)In: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 80, no 1, p. 153-184Article in journal (Refereed) Published
Abstract [en]

In this paper, a class of stochastic mathematical programs with probabilistic complementarity constraints is considered. We first investigate convergence properties of sample average approximation (SAA) approach to the corresponding chance constrained relaxed complementarity problem. Our discussion can be not only applied to the specific model in this paper, but also viewed as a supplementary for the SAA approach to general joint chance constrained problems. Furthermore, considering the uncertainty of the underlying probability distribution, a distributionally robust counterpart with a moment ambiguity set is proposed. The numerically tractable reformulation is derived. Finally, we use a production planing model to report some preliminary numerical results. 

Place, publisher, year, edition, pages
Springer Nature , 2021. Vol. 80, no 1, p. 153-184
Keywords [en]
Chance constraint, Complementarity problem, Distributionally robust, Sample average approximation, Stochastic programming, Stochastic systems, Chance-constrained, Complementarity constraint, Complementarity problems, Convergence properties, Numerical results, Numerically tractable, Stochastic mathematical programs, Probability distributions
National Category
Control Engineering Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-310141DOI: 10.1007/s10589-021-00292-5ISI: 000664814200001Scopus ID: 2-s2.0-85108594396OAI: oai:DiVA.org:kth-310141DiVA, id: diva2:1648240
Note

QC 20220330

Available from: 2022-03-30 Created: 2022-03-30 Last updated: 2022-06-25Bibliographically approved

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Peng, Shen

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