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Distributionally Robust Convex Optimization

Author

Listed:
  • Wolfram Wiesemann

    () (Imperial College Business School, Imperial College London, London SW7 2AZ, United Kingdom)

  • Daniel Kuhn

    () (College of Management and Technology, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland)

  • Melvyn Sim

    () (Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore 119077)

Abstract

Distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker’s prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions.

Suggested Citation

  • Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
  • Handle: RePEc:inm:oropre:v:62:y:2014:i:6:p:1358-1376
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    File URL: http://dx.doi.org/10.1287/opre.2014.1314
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    References listed on IDEAS

    as
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    17. David B. Brown & Melvyn Sim, 2009. "Satisficing Measures for Analysis of Risky Positions," Management Science, INFORMS, vol. 55(1), pages 71-84, January.
    18. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2009. "Constructing Risk Measures from Uncertainty Sets," Operations Research, INFORMS, vol. 57(5), pages 1129-1141, October.
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    3. Paul Embrechts & Alexander Schied & Ruodu Wang, 2018. "Robustness in the Optimization of Risk Measures," Papers 1809.09268, arXiv.org, revised Aug 2019.
    4. repec:eee:ejores:v:272:y:2019:i:3:p:832-846 is not listed on IDEAS
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    11. Patrick Jaillet & Jin Qi & Melvyn Sim, 2016. "Routing Optimization Under Uncertainty," Operations Research, INFORMS, vol. 64(1), pages 186-200, February.
    12. repec:eee:transb:v:119:y:2019:i:c:p:79-101 is not listed on IDEAS
    13. repec:spr:jglopt:v:70:y:2018:i:1:d:10.1007_s10898-017-0572-3 is not listed on IDEAS
    14. Amir Ardestani-Jaafari & Erick Delage, 2016. "Robust Optimization of Sums of Piecewise Linear Functions with Application to Inventory Problems," Operations Research, INFORMS, vol. 64(2), pages 474-494, April.
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    16. Viet Anh Nguyen & Daniel Kuhn & Peyman Mohajerin Esfahani, 2018. "Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator," Papers 1805.07194, arXiv.org.
    17. Napat Rujeerapaiboon & Daniel Kuhn & Wolfram Wiesemann, 2016. "Robust Growth-Optimal Portfolios," Management Science, INFORMS, vol. 62(7), pages 2090-2109, July.
    18. repec:eee:ejores:v:273:y:2019:i:2:p:740-753 is not listed on IDEAS
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