Ambiguous Joint Chance Constraints Under Mean and Dispersion Information

• 成果类型: Article
• 署名作者: Hanasusanto, Grani A.; Roitch, Vladimir; Kuhn, Daniel; Wiesemann, Wolfram
• 署名单位: University of Texas System; University of Texas Austin; University of Texas System; University of Texas Austin; Imperial College London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2016.1583
• 发表日期: 2017
• 页码: 751-767
• 关键词: PORTFOLIO OPTIMIZATION; robust solutions; uncertainty; approximations; PERSPECTIVE

摘要

We study joint chance constraints where the distribution of the uncertain parameters is only known to belong to an ambiguity set characterized by the mean and support of the uncertainties and by an upper bound on their dispersion. This setting gives rise to pessimistic (optimistic) ambiguous chance constraints, which require the corresponding classical chance constraints to be satisfied for every (for at least one) distribution in the ambiguity set. We demonstrate that the pessimistic joint chance constraints are conic representable if (i) the constraint coefficients of the decisions are deterministic, (ii) the support set of the uncertain parameters is a cone, and (iii) the dispersion function is of first order, that is, it is positively homogeneous. We also show that pessimistic joint chance constrained programs become intractable as soon as any of the conditions (i), (ii) or (iii) is relaxed in the mildest possible way. We further prove that the optimistic joint chance constraints are conic representable if (i) holds, and that they become intractable if (i) is violated. We show in numerical experiments that our results allow us to solve large-scale project management and image reconstruction models to global optimality.