co-radiant集的等价表示及其在向量优化问题中的应用

doi:10.15960/j.cnki.issn.1007-6093.2021.02.011

运筹学学报 ›› 2021, Vol. 25 ›› Issue (2): 135-143.doi: 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

汪文意¹, 高英¹, 刘芙萍¹^,*()

1. 重庆师范大学数学科学学院, 重庆 401331

收稿日期:2020-07-03 出版日期:2021-06-15 发布日期:2021-05-06
通讯作者: 刘芙萍 E-mail:lfp751214@163.com
作者简介:刘芙萍 E-mail: lfp751214@163.com
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

Wenyi WANG¹, Ying GAO¹, Fuping LIU¹^,*()

1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received:2020-07-03 Online:2021-06-15 Published:2021-05-06
Contact: Fuping LIU E-mail:lfp751214@163.com

摘要/Abstract

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。

关键词: co-radiant集, radiant集, 等价刻画, 多目标优化问题, 近似解

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.

Key words: co-radiant sets, radiant sets, equivalent representations, vector optimization problems, approximate solutions

中图分类号:

O221.6

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.

Wenyi WANG, Ying GAO, Fuping LIU. The equivalent representation of co-radiant sets and its application in multi-objective optimization problems[J]. Operations Research Transactions, 2021, 25(2): 135-143.

图/表 2

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[3]	张万里, 夏远梅, 赵克全. 向量优化中基于拟内部的弱C(\varepsilon)-有效解的标量化[J]. 运筹学学报, 2016, 20(2): 121-126.
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co-radiant集的等价表示及其在向量优化问题中的应用

The equivalent representation of co-radiant sets and its application in multi-objective optimization problems

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