Conic reformulations for Kullback-Leibler divergence constrained distributionally robust optimization and applications

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Kocuk, Burak (2021) Conic reformulations for Kullback-Leibler divergence constrained distributionally robust optimization and applications. International Journal of Optimization and Control: Theories and Applications, 11 (2). pp. 139-151. ISSN 2146-0957

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Abstract

In this paper, we consider a Kullback-Leibler divergence constrained distributionally robust optimization model. This model considers an ambiguity set that consists of all distributions whose Kullback-Leibler divergence to an empirical distribution is bounded. Utilizing the fact that this divergence measure has an exponential cone representation, we obtain the robust counterpart of the Kullback-Leibler divergence constrained distributionally robust optimization problem as a dual exponential cone constrained program under mild assumptions on the underlying optimization problem. The resulting conic reformulation of the original optimization problem can be directly solved by a commercial conic programming solver. We specialize our generic formulation to two classical optimization problems, namely, the Newsvendor Problem and the Uncapacitated Facility Location Problem. Our computational study in an out-of-sample analysis shows that the solutions obtained via the distributionally robust optimization approach yield significantly better performance in terms of the dispersion of the cost realizations while the central tendency deteriorates only slightly compared to the solutions obtained by stochastic programming.
Item Type: Article
Uncontrolled Keywords: Conic programming; Distributionally robust optimization; Newsvendor problem; Stochastic programming; Uncapacitated facility location problem
Divisions: Faculty of Engineering and Natural Sciences > Academic programs > Industrial Engineering
Faculty of Engineering and Natural Sciences
Depositing User: Burak Kocuk
Date Deposited: 03 Sep 2022 21:03
Last Modified: 03 Sep 2022 21:03
URI: https://research.sabanciuniv.edu/id/eprint/43472

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