Data-Driven Robust Chance Constrained Problems: A Mixture Model Approach

Zhiping Chen (), Shen Peng () and Jia Liu ()
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Zhiping Chen: Xi’an Jiaotong University
Shen Peng: Xi’an Jiaotong University
Jia Liu: Xi’an Jiaotong University

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 3, No 18, 1065-1085

Abstract: Abstract This paper discusses the mixture distribution-based data-driven robust chance constrained problem. We construct a data-driven mixture distribution-based uncertainty set from the perspective of simultaneously estimating higher-order moments. Then, we derive a reformulation of the data-driven robust chance constrained problem. As the reformulation is not a convex programming problem, we propose new and tight convex approximations based on the piecewise linear approximation method. We establish the theoretical foundation for these approximations. Finally, numerical results show that the proposed approximations are practical and efficient.

Keywords: Data-driven; Mixture distribution; Distributionally robust optimization; Chance constrained problem; Convex approximation; 90C15; 90C25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-018-1376-4

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