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Technical Note—Data-Driven Chance Constrained Programs over Wasserstein Balls

Author

Listed:
  • Zhi Chen

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

  • Daniel Kuhn

    (Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland)

  • Wolfram Wiesemann

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

Abstract

We provide an exact deterministic reformulation for data-driven, chance-constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand-side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the 1-norm or the ∞ -norm, the cone is the nonnegative orthant, and the chance-constrained program can be reformulated as a mixed-integer linear program. Our reformulation compares favorably to several state-of-the-art data-driven optimization schemes in our numerical experiments.

Suggested Citation

  • Zhi Chen & Daniel Kuhn & Wolfram Wiesemann, 2024. "Technical Note—Data-Driven Chance Constrained Programs over Wasserstein Balls," Operations Research, INFORMS, vol. 72(1), pages 410-424, January.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:1:p:410-424
    DOI: 10.1287/opre.2022.2330
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