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

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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.

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Acknowledgements

The authors are grateful to the relevant editors and two anonymous reviewers for their extremely detailed and insightful comments and suggestions, which have led to a substantial improvement of the paper in both content and style. This research was supported by the National Natural Science Foundation of China (Grant Nos. 11571270 and 71371152 ).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China

    Zhiping Chen, Shen Peng & Jia Liu

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  1. Zhiping Chen
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  2. Shen Peng
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  3. Jia Liu
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Correspondence to Zhiping Chen.

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Communicated by Evgeni A. Nurminski.

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Chen, Z., Peng, S. & Liu, J. Data-Driven Robust Chance Constrained Problems: A Mixture Model Approach. J Optim Theory Appl 179, 1065–1085 (2018). https://doi.org/10.1007/s10957-018-1376-4

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