运筹学学报 >
2021 , Vol. 25 >Issue 2: 135 - 143
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2021.02.011
co-radiant集的等价表示及其在向量优化问题中的应用
收稿日期: 2020-07-03
网络出版日期: 2021-05-06
基金资助
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)
The equivalent representation of co-radiant sets and its application in multi-objective optimization problems
Received date: 2020-07-03
Online published: 2021-05-06
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。
关键词： co-radiant集; radiant集; 等价刻画; 多目标优化问题; 近似解
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 . DOI: 10.15960/j.cnki.issn.1007-6093.2021.02.011
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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