Distributionally robust optimization with decision dependent ambiguity sets

Luo, Fengqiao; Mehrotra, Sanjay

doi:10.1007/s11590-020-01574-3

Cited by 71 publications

(44 citation statements)

References 54 publications

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“…Secondly, we would like to test the success of the proposed method on different problems with real datasets. Lastly, we may adapt our results to the decision-dependent setting, which is a recent active research area in the DRO literature [35,36,43].…”

Section: Discussionmentioning

confidence: 99%

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

Kocuk

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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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.

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Section: Discussionmentioning

confidence: 99%

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

Kocuk

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…Let x kω be the best feasible solution identified in solving CSub(y k , ω). Derive the scenario based optimality constraint (27) by solving (28). end for Solve the optimization (31) to obtain the current worst-case probability distribution p k .…”

Section: Generalization Of the Decomposition Methods For Dr-tss Mixed...mentioning

confidence: 99%

“…where x ω are the second-stage decision variables for scenario ω with l 1 integral and l 2 continuous variables, T ω is the technology matrix, and W ω is the recourse matrix corresponding to scenario ω. The algorithm developed in this paper was motivated from a distributionally-robust generalization of a service center location problem with decision-dependent customer utilities studied in our recent work [1]. This model will be considered in our computational study.…”

Section: Introductionmentioning

confidence: 99%

A Decomposition Method for Distributionally-Robust Two-stage Stochastic Mixed-integer Cone Programs

Luo,

Mehrotra

2019

Preprint

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We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, and its important special case of distributionally-robust two-stage stochastic mixed-integer second order cone programs. This generalizes the algorithm proposed by Sen and Sherali [Mathematical Programming 106(2): 203-223, 2006]. We show that the proposed algorithm is finitely convergent if the second-stage problems are solved to optimality at incumbent first stage solutions, and solution to an optimization problem to identify worst-case probability distribution is available. The second stage problems can be solved using a branch-and-cut algorithm. The decomposition algorithm is illustrated with an example. Computational results on a stochastic programming generalization of a facility location problem show significant solution time improvements from the proposed approach. Solutions for many models that are intractable for an extensive form formulation become possible. Computational results suggest that solution time requirement does not increase significantly when considering distributional robust counterparts to the stochastic programming models.

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“…KS-test is widely used in hypothesis testing for the comparison of the cumulative distribution functions (cdf) of given distributions [77], [78]. Suppose the real and generated data have a size of R and G samples, respectively.…”

Section: Data Generationmentioning

confidence: 99%