On Distributionally Robust Chance-Constrained Linear Programs

Download: .pdf

Authors: G. C. Calafiore and L. El Ghaoui.

Status: Jour. of Optimization Theory and Applications, vol. 130, no. 1, pp. 1-22, July 2006.

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 dis- tributions) 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.

Related entries:
- Linear programming with probability constraints — part I, Proc. American Control Conf., July 2007.
- Linear programming with probability constraints — part II, Proc. American Control Conf., July 2007.

Bibtex reference:

@article{CaE:06,
	Author = {G. C. Calafiore and L. {El Ghaoui}},
	Journal = {Jour. of Optimization Theory and Applications},
	Month = dec,
	Number = {1},
	Title = {On Distributionally Robust Chance-Constrained Linear Programs},
	Volume = {130},
	Year = {2006}}