IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v313y2024i2p616-627.html
   My bibliography  Save this article

Mathematical programs with distributionally robust chance constraints: Statistical robustness, discretization and reformulation

Author

Listed:
  • Jiang, Jie
  • Peng, Shen

Abstract

In this paper, we consider mathematical programs with distributionally robust chance constraints (MPDRCC), where the ambiguity set is given by the general moment information. From the contaminated data-driven viewpoint, we first study the qualitative statistical robustness of MPDRCC. Then, motivated by the computational tractability, we investigate the discrete approximation of MPDRCC. The corresponding convergence results of the optimal value and the optimal solution set of the discrete approximation problem are established. After that, a reformulation of the discrete approximation problem is presented under standard assumptions, which is applied to solve MPDRCC approximately according to the above convergence results. Finally, two applications are reported, and some numerical results show that the statistical robustness assertion and the discrete approximation scheme are practical and effective.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:313:y:2024:i:2:p:616-627
    DOI: 10.1016/j.ejor.2023.10.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723007956
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.10.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hailin Sun & Huifu Xu, 2016. "Convergence Analysis for Distributionally Robust Optimization and Equilibrium Problems," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 377-401, May.
    2. Wei Wang & Huifu Xu & Tiejun Ma, 2021. "Quantitative statistical robustness for tail-dependent law invariant risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 21(10), pages 1669-1685, October.
    3. 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.
    4. Volker Krätschmer & Alexander Schied & Henryk Zähle, 2014. "Comparative and qualitative robustness for law-invariant risk measures," Finance and Stochastics, Springer, vol. 18(2), pages 271-295, April.
    5. Pafka, Szilárd & Kondor, Imre, 2003. "Noisy covariance matrices and portfolio optimization II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 487-494.
    6. 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.
    7. Volker Kratschmer & Alexander Schied & Henryk Zahle, 2012. "Comparative and qualitative robustness for law-invariant risk measures," Papers 1204.2458, arXiv.org, revised Jan 2014.
    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. Zaghian, Maryam & Lim, Gino J. & Khabazian, Azin, 2018. "A chance-constrained programming framework to handle uncertainties in radiation therapy treatment planning," European Journal of Operational Research, Elsevier, vol. 266(2), pages 736-745.
    10. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    11. 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.
    12. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2017. "Domains of weak continuity of statistical functionals with a view toward robust statistics," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 1-19.
    13. 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.
    14. Yongchao Liu & Alois Pichler & Huifu Xu, 2019. "Discrete Approximation and Quantification in Distributionally Robust Optimization," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 19-37, February.
    15. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2012. "Qualitative and infinitesimal robustness of tail-dependent statistical functionals," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 35-47, January.
    16. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
    17. B. K. Pagnoncelli & S. Ahmed & A. Shapiro, 2009. "Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 399-416, August.
    18. Ran Ji & Miguel A. Lejeune, 2021. "Data-driven distributionally robust chance-constrained optimization with Wasserstein metric," Journal of Global Optimization, Springer, vol. 79(4), pages 779-811, April.
    19. Feifeng Zheng & Zhaojie Wang & E. Zhang & Ming Liu, 2022. "Distributionally Robust Joint Chance Constrained Vessel Fleet Deployment Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(06), pages 1-19, December.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sainan Zhang & Huifu Xu, 2022. "Insurance premium-based shortfall risk measure induced by cumulative prospect theory," Computational Management Science, Springer, vol. 19(4), pages 703-738, October.
    2. 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.
    3. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Ruodu Wang, 2017. "Risk bounds for factor models," Finance and Stochastics, Springer, vol. 21(3), pages 631-659, July.
    4. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.
    5. Zähle, Henryk, 2016. "A definition of qualitative robustness for general point estimators, and examples," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 12-31.
    6. Fissler Tobias & Ziegel Johanna F., 2021. "On the elicitability of range value at risk," Statistics & Risk Modeling, De Gruyter, vol. 38(1-2), pages 25-46, January.
    7. Koch-Medina Pablo & Munari Cosimo, 2014. "Law-invariant risk measures: Extension properties and qualitative robustness," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 215-236, December.
    8. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2017. "Domains of weak continuity of statistical functionals with a view toward robust statistics," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 1-19.
    9. Yannan Chen & Hailin Sun & Huifu Xu, 2021. "Decomposition and discrete approximation methods for solving two-stage distributionally robust optimization problems," Computational Optimization and Applications, Springer, vol. 78(1), pages 205-238, January.
    10. Krätschmer Volker & Schied Alexander & Zähle Henryk, 2015. "Quasi-Hadamard differentiability of general risk functionals and its application," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 25-47, April.
    11. M. Burzoni & I. Peri & C. M. Ruffo, 2017. "On the properties of the Lambda value at risk: robustness, elicitability and consistency," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1735-1743, November.
    12. Zou, Zhenfeng & Wu, Qinyu & Xia, Zichao & Hu, Taizhong, 2023. "Adjusted Rényi entropic Value-at-Risk," European Journal of Operational Research, Elsevier, vol. 306(1), pages 255-268.
    13. Guanglin Xu & Samuel Burer, 2018. "A data-driven distributionally robust bound on the expected optimal value of uncertain mixed 0-1 linear programming," Computational Management Science, Springer, vol. 15(1), pages 111-134, January.
    14. 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.
    15. Ruodu Wang & Johanna F. Ziegel, 2014. "Distortion Risk Measures and Elicitability," Papers 1405.3769, arXiv.org, revised May 2014.
    16. Jie Jiang, 2024. "Distributionally Robust Variational Inequalities: Relaxation, Quantification and Discretization," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 227-255, October.
    17. Sally G. Arcidiacono & Damiano Rossello, 2022. "A hybrid approach to the discrepancy in financial performance’s robustness," Operational Research, Springer, vol. 22(5), pages 5441-5476, November.
    18. Tobias Fissler & Johanna F. Ziegel, 2015. "Higher order elicitability and Osband's principle," Papers 1503.08123, arXiv.org, revised Sep 2015.
    19. Matteo Burzoni & Ilaria Peri & Chiara Maria Ruffo, 2016. "On the properties of the Lambda value at risk: robustness, elicitability and consistency," Papers 1603.09491, arXiv.org, revised Feb 2017.
    20. Yue Zhao & Zhi Chen & Zhenzhen Zhang, 2023. "Distributionally Robust Chance-Constrained p -Hub Center Problem," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1361-1382, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:313:y:2024:i:2:p:616-627. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.