期刊
MATHEMATICS OF OPERATIONS RESEARCH
卷 -, 期 -, 页码 -出版社
INFORMS
DOI: 10.1287/moor.2021.1233
关键词
geometric optimization; distributionally robust; chance constraints; uncertainty sets
资金
- Campus France-CSC Cai Yuanpei program [34593YE]
- National Natural Science Foundation of China [11901449, 11991023]
This paper discusses distributionally robust geometric programs with individual or joint chance constraints, considering several groups of uncertainty sets. Deterministic reformulations of the programs are found under each group of uncertainty sets. Convexity, solution methods, and relationships of the reformulation programs are discussed. Numerical tests are carried out on a shape optimization problem.
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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