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Adjustable Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

Author

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  • Haolin Ruan

    (School of Data Science, City University of Hong Kong, Kowloon Tong, Hong Kong)

  • Zhi Chen

    (Department of Management Sciences, College of Business, City University of Hong Kong, Kowloon Tong, Hong Kong)

  • Chin Pang Ho

    (School of Data Science, City University of Hong Kong, Kowloon Tong, Hong Kong)

Abstract

We study adjustable distributionally robust optimization problems, where their ambiguity sets can potentially encompass an infinite number of expectation constraints. Although such ambiguity sets have great modeling flexibility in characterizing uncertain probability distributions, the corresponding adjustable problems remain computationally intractable and challenging. To overcome this issue, we propose a greedy improvement procedure that consists of solving, via the (extended) linear decision rule approximation, a sequence of tractable subproblems—each of which considers a relaxed and finitely constrained ambiguity set that can be iteratively tightened to the infinitely constrained one. Through three numerical studies of adjustable distributionally robust optimization models, we show that our approach can yield improved solutions in a systematic way for both two-stage and multistage problems.

Suggested Citation

  • Haolin Ruan & Zhi Chen & Chin Pang Ho, 2023. "Adjustable Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1002-1023, September.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:5:p:1002-1023
    DOI: 10.1287/ijoc.2021.0181
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    References listed on IDEAS

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    1. Ketkov, Sergey S., 2024. "A study of distributionally robust mixed-integer programming with Wasserstein metric: on the value of incomplete data," European Journal of Operational Research, Elsevier, vol. 313(2), pages 602-615.

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