Distributionally Robust Linear and Discrete Optimization with Marginals

Chen, Louis; Ma, Will; Natarajan, Karthik; Simchi‐Levi, David; Yan, Zhenzhen

doi:10.2139/ssrn.3159473

Cited by 10 publications

(14 citation statements)

References 29 publications

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“…Discrete problems. Chen et al [69] study a problem of the form (1.5), where the cost function h(x, ξ) denotes the optimal value of a linear or discrete optimization problem with random linear objective coefficients. They assume the ambiguity set of distribution is formed by all distributions with known marginals.…”

Section: Marginals (Fréchet)mentioning

confidence: 99%

Distributionally Robust Optimization: A Review

Rahimian,

Mehrotra

2019

Preprint

131

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: Marginals (Fréchet)mentioning

confidence: 99%

Distributionally Robust Optimization: A Review

Rahimian,

Mehrotra

2019

Preprint

131

196

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“…Shen 2014), disruption risks in facility location (Lu et al 2015), random capacity in multi-sourcing Freeman 2016, 2018), and service times in appointment scheduling (Chen et al 2018a).…”

Section: Author Manuscriptmentioning

confidence: 99%

A Review of Robust Operations Management under Model Uncertainty

Shen

2021

Production and Operations Management

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“…The MMOT problem serves as the basis of other related problems such as the Wasserstein barycenter problem [2] and the martingale optimal transport problem [5]. The original MMOT problem and its various extensions have many modern theoretical and practical applications, including but not limited to: theoretical economics [13,18,31], density functional theory (DFT) in quantum mechanics [12,15,20,21], computational fluid mechanics [7,9], mathematical finance [5,17,23,25,29,38,40], statistics [53,54], machine learning [51], tomographic image reconstruction [1], signal processing [30,39], and operations research [16,32,33].…”

Section: Introductionmentioning

confidence: 99%

Numerical method for feasible and approximately optimal solutions of multi-marginal optimal transport beyond discrete measures

Neufeld¹,

Xiang²

2022

Preprint

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We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general measures that are not necessarily discrete. By developing a relaxation scheme in which marginal constraints are replaced by finitely many linear constraints and by proving a specifically tailored duality result for this setting, we approximate the MMOT problem by a linear semiinfinite optimization problem. Moreover, we are able to recover a feasible and approximately optimal solution of the MMOT problem, and its sub-optimality can be controlled to be arbitrarily close to 0 under mild conditions. The developed relaxation scheme leads to a numerical algorithm which can compute a feasible approximate optimizer of the MMOT problem whose theoretical sub-optimality can be chosen to be arbitrarily small. Besides the approximate optimizer, the algorithm is also able to compute both an upper bound and a lower bound on the optimal value of the MMOT problem. The difference between the computed bounds provides an explicit upper bound on the sub-optimality of the computed approximate optimizer. Through a numerical example, we demonstrate that the proposed algorithm is capable of computing a high-quality solution of an MMOT problem involving as many as 50 marginals along with an explicit estimate of its sub-optimality that is much less conservative compared to the theoretical estimate.

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Distributionally Robust Linear and Discrete Optimization with Marginals

Cited by 10 publications

References 29 publications

Distributionally Robust Optimization: A Review

Distributionally Robust Optimization: A Review

A Review of Robust Operations Management under Model Uncertainty

Numerical method for feasible and approximately optimal solutions of multi-marginal optimal transport beyond discrete measures

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