IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v130y2006i1d10.1007_s10957-006-9084-x.html
   My bibliography  Save this article

On Distributionally Robust Chance-Constrained Linear Programs

Author

Listed:
  • G. C. Calafiore

    (Politecnico di Torino)

  • L. El Ghaoui

    (University of California at Berkeley)

Abstract

In this paper, we discuss linear programs in which the data that specify the constraints are subject to random uncertainty. A usual approach in this setting is to enforce the constraints up to a given level of probability. We show that, for a wide class of probability distributions (namely, radial distributions) on the data, the probability constraints can be converted explicitly into convex second-order cone constraints; hence, the probability-constrained linear program can be solved exactly with great efficiency. Next, we analyze the situation where the probability distribution of the data is not completely specified, but is only known to belong to a given class of distributions. In this case, we provide explicit convex conditions that guarantee the satisfaction of the probability constraints for any possible distribution belonging to the given class.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:1:d:10.1007_s10957-006-9084-x
    DOI: 10.1007/s10957-006-9084-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9084-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-006-9084-x?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. Bertsimas, Dimitris. & Popescu, Ioana., 1998. "Optimal inequalities in probability theory : a convex optimization approach," Working papers WP 4025-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    3. C. van de Panne & W. Popp, 1963. "Minimum-Cost Cattle Feed Under Probabilistic Protein Constraints," Management Science, INFORMS, vol. 9(3), pages 405-430, April.
    4. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    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. T Peña & P Lara & C Castrodeza, 2009. "Multiobjective stochastic programming for feed formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1738-1748, December.
    2. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    3. Avik Pradhan & M. P. Biswal, 2017. "Multi-choice probabilistic linear programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 122-142, March.
    4. Ioana Popescu, 2007. "Robust Mean-Covariance Solutions for Stochastic Optimization," Operations Research, INFORMS, vol. 55(1), pages 98-112, February.
    5. Maxime C. Cohen & Philipp W. Keller & Vahab Mirrokni & Morteza Zadimoghaddam, 2019. "Overcommitment in Cloud Services: Bin Packing with Chance Constraints," Management Science, INFORMS, vol. 65(7), pages 3255-3271, July.
    6. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    7. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    8. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    9. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    10. Zhang, Nan & Jin, Zhuo & Li, Shuanming & Chen, Ping, 2016. "Optimal reinsurance under dynamic VaR constraint," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 232-243.
    11. Hang Li & Zhe Zhang & Xianggen Yin & Buhan Zhang, 2020. "Preventive Security-Constrained Optimal Power Flow with Probabilistic Guarantees," Energies, MDPI, vol. 13(9), pages 1-13, May.
    12. Wu, Desheng (Dash) & Lee, Chi-Guhn, 2010. "Stochastic DEA with ordinal data applied to a multi-attribute pricing problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1679-1688, December.
    13. Barrieu, Pauline & Scandolo, Giacomo, 2014. "Assessing financial model risk," LSE Research Online Documents on Economics 60084, London School of Economics and Political Science, LSE Library.
    14. Xuejie Bai & Yankui Liu, 2016. "Robust optimization of supply chain network design in fuzzy decision system," Journal of Intelligent Manufacturing, Springer, vol. 27(6), pages 1131-1149, December.
    15. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    16. Giada Spaccapanico Proietti & Mariagiulia Matteucci & Stefania Mignani & Bernard P. Veldkamp, 2024. "Chance-Constrained Automated Test Assembly," Journal of Educational and Behavioral Statistics, , vol. 49(1), pages 92-120, February.
    17. Viet Anh Nguyen & Fan Zhang & Shanshan Wang & Jose Blanchet & Erick Delage & Yinyu Ye, 2021. "Robustifying Conditional Portfolio Decisions via Optimal Transport," Papers 2103.16451, arXiv.org, revised Apr 2024.
    18. Guigues, Vincent & Juditsky, Anatoli & Nemirovski, Arkadi, 2021. "Constant Depth Decision Rules for multistage optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 295(1), pages 223-232.
    19. Torres-Rojo, J. M., 2001. "Risk management in the design of a feeding ration: a portfolio theory approach," Agricultural Systems, Elsevier, vol. 68(1), pages 1-20, April.
    20. Humphery-Jenner, M., 2011. "Anti-takeover Provisions as a Source of Innovation and Value Creation," Discussion Paper 2011-045, Tilburg University, Center for Economic Research.

    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:spr:joptap:v:130:y:2006:i:1:d:10.1007_s10957-006-9084-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.