Stochastic mathematical programs with probabilistic complementarity constraints: SAA and distributionally robust approaches

Shen Peng () and Jie Jiang ()
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Shen Peng: KTH Royal Institute of Technology
Jie Jiang: Chongqing University

Computational Optimization and Applications, 2021, vol. 80, issue 1, No 6, 153-184

Abstract: Abstract 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.

Keywords: Stochastic programming; Complementarity problem; Chance constraint; Sample average approximation; Distributionally robust; 90C15; 90C33; 90C25 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-021-00292-5

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