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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
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