Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets
Distributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introduce a novel class of DRO challenges where the proba...
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2024-10-01
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| author | Jie Zhang Shuang Lin Yifei Wang |
| author_facet | Jie Zhang Shuang Lin Yifei Wang |
| author_sort | Jie Zhang |
| collection | DOAJ |
| description | Distributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introduce a novel class of DRO challenges where the probability distribution of random variables is contingent upon the decision variables, and the ambiguity set is defined through parameterization involving the mean and a covariance matrix, which also depend on the decision variables. This dependency makes DRO difficult to solve directly; therefore, first, we demonstrate that under the condition of a full-space support set, the original problem can be reduced to a second-order cone programming (SOCP) problem. Subsequently, we solve this second-order cone programming problem using a projection differential equation approach. Compared with the traditional methods, the differential equation method offers advantages in providing continuous and smooth solutions, offering inherent stability analysis, and possessing a rich mathematical toolbox, which make the differential equation a powerful and versatile tool for addressing complex optimization challenges. |
| format | Article |
| id | doaj-art-52c825872e83422eb9e997f320528b74 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-52c825872e83422eb9e997f320528b742025-08-20T02:11:04ZengMDPI AGAxioms2075-16802024-10-01131069910.3390/axioms13100699Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty SetsJie Zhang0Shuang Lin1Yifei Wang2School of Mathematics, Liaoning Normal University, Dalian 116029, ChinaDepartment of Basic Courses Teaching, Dalian Polytechnic University, Dalian 116034, ChinaSchool of Mathematics, Liaoning Normal University, Dalian 116029, ChinaDistributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introduce a novel class of DRO challenges where the probability distribution of random variables is contingent upon the decision variables, and the ambiguity set is defined through parameterization involving the mean and a covariance matrix, which also depend on the decision variables. This dependency makes DRO difficult to solve directly; therefore, first, we demonstrate that under the condition of a full-space support set, the original problem can be reduced to a second-order cone programming (SOCP) problem. Subsequently, we solve this second-order cone programming problem using a projection differential equation approach. Compared with the traditional methods, the differential equation method offers advantages in providing continuous and smooth solutions, offering inherent stability analysis, and possessing a rich mathematical toolbox, which make the differential equation a powerful and versatile tool for addressing complex optimization challenges.https://www.mdpi.com/2075-1680/13/10/699DROSOCPdecision-dependent ambiguity setprojection differential equation approach |
| spellingShingle | Jie Zhang Shuang Lin Yifei Wang Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets Axioms DRO SOCP decision-dependent ambiguity set projection differential equation approach |
| title | Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets |
| title_full | Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets |
| title_fullStr | Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets |
| title_full_unstemmed | Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets |
| title_short | Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets |
| title_sort | reformulation and enhancement of distributed robust optimization framework incorporating decision adaptive uncertainty sets |
| topic | DRO SOCP decision-dependent ambiguity set projection differential equation approach |
| url | https://www.mdpi.com/2075-1680/13/10/699 |
| work_keys_str_mv | AT jiezhang reformulationandenhancementofdistributedrobustoptimizationframeworkincorporatingdecisionadaptiveuncertaintysets AT shuanglin reformulationandenhancementofdistributedrobustoptimizationframeworkincorporatingdecisionadaptiveuncertaintysets AT yifeiwang reformulationandenhancementofdistributedrobustoptimizationframeworkincorporatingdecisionadaptiveuncertaintysets |