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Distributionally Robust Chance Constrained Geometric Optimization

Author

Listed:
  • Jia Liu

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China; Center for Optimization Technique and Quantitative Finance, Xi’an International Academy for Mathematics and Mathematical Technology, Xi’an 710049, China)

  • Abdel Lisser

    (Université Paris Saclay, CNRS, CentraleSupelec, Laboratoire des Signaux et des Systèmes, 91190 Gif-sur-Yvette, France)

  • Zhiping Chen

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China; Center for Optimization Technique and Quantitative Finance, Xi’an International Academy for Mathematics and Mathematical Technology, Xi’an 710049, China)

Abstract

This paper discusses distributionally robust geometric programs with individual or joint chance constraints. Several groups of uncertainty sets are considered: uncertainty sets with first two order moments information; uncertainty sets with known first order or first two order moments information under nonnegative support; uncertainty sets constrained by the Kullback–Leibler divergence with a normal or discrete reference distribution; uncertainty sets constrained by the Wasserstein distance under discrete, full, or nonnegative real-space support; and joint uncertainty sets for the product of random variables. Under each group of uncertainty sets, we find deterministic reformulations of the distributionally robust geometric programs with individual or joint chance constraints. Convexity, solution methods, and relationships of the reformulation programs are discussed. Finally, numerical tests are carried out on a shape optimization problem.

Suggested Citation

  • Jia Liu & Abdel Lisser & Zhiping Chen, 2022. "Distributionally Robust Chance Constrained Geometric Optimization," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 2950-2988, November.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:4:p:2950-2988
    DOI: 10.1287/moor.2021.1233
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