| co-radiant集的等价表示及其在向量优化问题中的应用 |
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| 引用本文： | 汪文意,高英,刘芙萍.co-radiant集的等价表示及其在向量优化问题中的应用[J].运筹学学报,2021,25(2):135-143. |
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| 作者姓名： | 汪文意 高英 刘芙萍 |
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| 作者单位： | 1. 重庆师范大学数学科学学院, 重庆 401331 |
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| 基金项目： | 国家自然科学基金(11771064);国家自然科学基金(11991024);重庆市科学技术研究重点项目(KJZDK202001104);重庆市高校创新研究群体项目(CXQT20014) |
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| 摘 要： | 作为特殊的抽象凸(凹)集，radiant集和co-radiant集在抽象凸分析和多目标优化问题理论中发挥着重要作用。首先建立radiant集co-radiant集的等价刻画，从而推导出它们的重要性质。然后，将重要性质应用到向量优化问题近似解的刻画中，得到关于近似解集的等价刻画。
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| 关 键 词： | co-radiant集 radiant集 等价刻画 多目标优化问题 近似解 |
| 收稿时间： | 2020-07-03 |
The equivalent representation of co-radiant sets and its application in multi-objective optimization problems |
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| Wenyi WANG,Ying GAO,Fuping LIU.The equivalent representation of co-radiant sets and its application in multi-objective optimization problems[J].OR Transactions,2021,25(2):135-143. |
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| Authors: | Wenyi WANG Ying GAO Fuping LIU |
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| Institution: | 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China |
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| Abstract: | As a special abstract convex (concave) sets, radiant sets and co-radiant sets play the important roles in abstract convex analysis and the theory of multiobjective optimization problems. We first establish the equivalent characterizations for the radiant sets and co-radiant sets. Finally, we apply important properties to the characterization of the approximate solutions of the vector optimization problems, and obtain the equivalent characterization of the approximate solution sets. |
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| Keywords: | co-radiant sets radiant sets equivalent representations vector optimization problems approximate solutions |
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