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

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  • Zhiping Chen

    (Xi’an Jiaotong University)

  • Shen Peng

    (Xi’an Jiaotong University)

  • Jia Liu

    (Xi’an Jiaotong University)

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.

Suggested Citation

  • Zhiping Chen & Shen Peng & Jia Liu, 2018. "Data-Driven Robust Chance Constrained Problems: A Mixture Model Approach," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1065-1085, December.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:3:d:10.1007_s10957-018-1376-4
    DOI: 10.1007/s10957-018-1376-4
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    References listed on IDEAS

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    Cited by:

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