Distributionally Robust Chance Constrained Geometric Optimization - CentraleSupélec
Article Dans Une Revue Mathematics of Operations Research Année : 2022

Distributionally Robust Chance Constrained Geometric Optimization

Jia Liu
Abdel Lisser
Zhiping Chen

Résumé

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.
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Dates et versions

hal-04488061 , version 1 (04-03-2024)

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Citer

Jia Liu, Abdel Lisser, Zhiping Chen. Distributionally Robust Chance Constrained Geometric Optimization. Mathematics of Operations Research, 2022, 47 (4), pp.2950-2988. ⟨10.1287/moor.2021.1233⟩. ⟨hal-04488061⟩
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