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Distributionally Robust Optimization with Polynomial Robust Constraints

Author

Listed:
  • Jiawang Nie

    (University of California San Diego)

  • Suhan Zhong

    (Texas A&M University)

Abstract

This paper studies distributionally robust optimization (DRO) with polynomial robust constraints. We give a Moment-SOS relaxation approach to solve the DRO. This reduces to solving linear conic optimization with semidefinite constraints. When the DRO problem is SOS-convex, we show that it is equivalent to the linear conic relaxation and it can be solved by the Moment-SOS algorithm. For nonconvex cases, we also give concrete conditions such that the DRO can be solved globally. Numerical experiments are given to show the efficiency of the method.

Suggested Citation

  • Jiawang Nie & Suhan Zhong, 2025. "Distributionally Robust Optimization with Polynomial Robust Constraints," Journal of Global Optimization, Springer, vol. 92(3), pages 509-534, July.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:3:d:10.1007_s10898-025-01504-6
    DOI: 10.1007/s10898-025-01504-6
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    References listed on IDEAS

    as
    1. Linwei Xin & David Alan Goldberg, 2022. "Distributionally Robust Inventory Control When Demand Is a Martingale," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 2387-2414, August.
    2. Yannan Chen & Hailin Sun & Huifu Xu, 2021. "Decomposition and discrete approximation methods for solving two-stage distributionally robust optimization problems," Computational Optimization and Applications, Springer, vol. 78(1), pages 205-238, January.
    3. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.
    4. Jiawang Nie, 2011. "Polynomial Matrix Inequality and Semidefinite Representation," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 398-415, August.
    5. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    6. Dimitris Bertsimas & Melvyn Sim & Meilin Zhang, 2019. "Adaptive Distributionally Robust Optimization," Management Science, INFORMS, vol. 65(2), pages 604-618, February.
    7. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
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    Cited by:

    1. Gabriele Visentin & Patrick Cheridito, 2025. "Robust Optimization in Causal Models and G-Causal Normalizing Flows," Papers 2510.15458, arXiv.org.

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