On solving two-stage distributionally robust disjunctive programs with a general ambiguity set

Bansal, Manish; Mehrotra, Sanjay

doi:10.1016/j.ejor.2019.05.033

Cited by 13 publications

(14 citation statements)

References 39 publications

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“…As Theorem 3.12, we can rewrite the inner problem of a model of the form (1.5) with φ-divergences as the expected cost plus a regularization term that accounts for the standard deviation of the cost, under the empirical distribution. Reformulation (4.1) is a semi-infinite program (SIP), and at a first glance, obtaining an optimal solution to this problem looks unreachable 10 . It is well-known that even convex SIPs cannot be solved directly with numerical methods, and in particular are not amenable to the use of methods such as interior point method.…”

Section: 4mentioning

confidence: 99%

“…Bansal and Mehrotra [10] introduce two-stage distributionally robust disjunctive programs with disjunctive constraints in both stages and a general ambiguity set for the probability distributions. To solve the resulting model, they develop decomposition algorithms, which utilize Balas' linear programming equivalent for deterministic disjunctive programs or his sequential convexification approach within the L-shaped method.…”

Section: Shape-preserving Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Distributionally Robust Optimization: A Review

Rahimian,

Mehrotra

2019

Preprint

Self Cite

139

196

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The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization.

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Section: 4mentioning

confidence: 99%

Section: Shape-preserving Modelsmentioning

confidence: 99%

Distributionally Robust Optimization: A Review

Rahimian,

Mehrotra

2019

Preprint

Self Cite

139

196

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show abstract

“…Reformulation ( 17) is a semi-infinite program (SIP), and at a first glance, obtaining an optimal solution to this problem looks difficult 13 . It is well-known that even convex SIPs cannot be solved directly with numerical 12 One can similarly define the φ-divergence between two probability distributions P1 and P2 induced by ξ.…”

Section: General Solution Techniques To Solve Dro Modelsmentioning

confidence: 99%

Frameworks and Results in Distributionally Robust Optimization

Rahimian¹,

Mehrotra²

2022

Open Journal of Mathematical Optimization

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The concepts of risk aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. The statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and relationships with robust optimization, risk aversion, chance-constrained optimization, and function regularization. Various approaches to model the distributional ambiguity and their calibrations are discussed. The paper also describes the main solution techniques used to the solve the resulting optimization problems.

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“…The Benders' decomposition algorithms developed for two-stage stochastic mixed integer programs with binary first stage variables can be modified to solve distributionally-robust two-stage stochastic mixed integer programs [22], and distributionally robust two-stage stochastic disjunctive programs [23]. The algorithms retain their finite-convergence property if the ambiguity set is polyhedral representable [22], or more generally when a separation oracle for the unknown probability distribution is available [23].…”

Section: Introductionmentioning

confidence: 99%

“…The work in this paper is most closely related to [15], while it benefits from the observations in [22,23]. This paper makes the following contributions.…”

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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On solving two-stage distributionally robust disjunctive programs with a general ambiguity set

Cited by 13 publications

References 39 publications

Distributionally Robust Optimization: A Review

Distributionally Robust Optimization: A Review

Frameworks and Results in Distributionally Robust Optimization

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

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