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On Distributionally Robust Chance-Constrained Linear Programs

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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.

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Authors and Affiliations

  1. Dipartimento di Automatica e Informatica, Politecnico di Torino, Torino, Italy

    G. C. Calafiore (Associate Professor)

  2. Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, California

    L. El Ghaoui (Associate Professor)

Authors
  1. G. C. Calafiore
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  2. L. El Ghaoui
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Additional information

Communicated by B. T. Polyak

This work was supported by FIRB funds from the Italian Ministry of University and Research.

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Calafiore, G.C., Ghaoui, L.E. On Distributionally Robust Chance-Constrained Linear Programs. J Optim Theory Appl 130, 1–22 (2006). https://doi.org/10.1007/s10957-006-9084-x

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  • DOI: https://doi.org/10.1007/s10957-006-9084-x

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