带参数集值向量优化问题ε-超有效点集的连通性
Connectedness of ε-Super Effective Point Set for Set-Valued Vector Optimization Problems with Parameters
DOI: 10.12677/PM.2022.123040, PDF,    国家自然科学基金支持
作者: 章 勤, 陈剑尘, 邢秋菊*：南昌航空大学数学与信息科学学院，江西 南昌
关键词: 连通性；集值映射；带参数ε-超有效点；Connectedness； Set-Valued Mapping； ε-Super Effective Points with Parameters
摘要: 本文主要研究了带参数ε-超有效点集的连通性。首先在局部凸的Hausdorff拓扑线性空间中引进了带参数的ε-超有效点集的概念，然后在可行域为弧连通紧的，目标函数为C-弧连通的集值映射的情况下，证明了ε-超有效点集非空并得到了带参数的ε-超有效点集的连通性。
Abstract: In this paper, we study the connectivity of ε-super effective point sets with parameters. Firstly we introduce the concept of ε-super effective point set with parameters in locally convex Hausdorff topological linear space. Then, under the condition that the feasible region is arcwise connected and compact, and the objective function is C-arcwise connected set-valued mapping, we prove the ε-super effective point set is nonempty and obtain the connectedness of ε-super efficient solution set with parameters.
文章引用：章勤, 陈剑尘, 邢秋菊. 带参数集值向量优化问题ε-超有效点集的连通性[J]. 理论数学, 2022, 12(3): 368-375. https://doi.org/10.12677/PM.2022.123040

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