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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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    1. Bruce L. Miller & Harvey M. Wagner, 1965. "Chance Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 13(6), pages 930-945, December.
    2. Hall, Joyce A. & Brorsen, B. Wade & Irwin, Scott H., 1989. "The Distribution of Futures Prices: A Test of the Stable Paretian and Mixture of Normals Hypotheses," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(1), pages 105-116, March.
    3. R. Jagannathan, 1974. "Chance-Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 22(2), pages 358-372, April.
    4. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    5. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.
    6. Zhu, Shushang & Fan, Minjie & Li, Duan, 2014. "Portfolio management with robustness in both prediction and decision: A mixture model based learning approach," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 1-25.
    7. McCauley,Joseph L., 2009. "Dynamics of Markets," Cambridge Books, Cambridge University Press, number 9780521429627, January.
    8. G. C. Calafiore & L. El Ghaoui, 2006. "On Distributionally Robust Chance-Constrained Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 1-22, July.
    9. Grani A. Hanasusanto & Vladimir Roitch & Daniel Kuhn & Wolfram Wiesemann, 2017. "Ambiguous Joint Chance Constraints Under Mean and Dispersion Information," Operations Research, INFORMS, vol. 65(3), pages 751-767, June.
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    Cited by:

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    2. Berndt Jesenko & Christian Schlögl, 2021. "The effect of web of science subject categories on clustering: the case of data-driven methods in business and economic sciences," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(8), pages 6785-6801, August.
    3. Shen Peng & Jie Jiang, 2021. "Stochastic mathematical programs with probabilistic complementarity constraints: SAA and distributionally robust approaches," Computational Optimization and Applications, Springer, vol. 80(1), pages 153-184, September.
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    5. Zhiping Chen & Shen Peng & Abdel Lisser, 2020. "A sparse chance constrained portfolio selection model with multiple constraints," Journal of Global Optimization, Springer, vol. 77(4), pages 825-852, August.
    6. Jiang, Jie & Peng, Shen, 2024. "Mathematical programs with distributionally robust chance constraints: Statistical robustness, discretization and reformulation," European Journal of Operational Research, Elsevier, vol. 313(2), pages 616-627.

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