带约束映射的ε-强有效点集的连通性  

Connectedness ofε-strong Efficient Point Set for Set-valued Optimization Problems with Constraints

作　　者：章勤 陈剑尘[1] 吴昌耀 邢秋菊 ZHANG Qin;CHEN Jian-chen;WU Chang-yao;XING Qiu-ju(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2022年第1期23-27,共5页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(11061023);江西省自然科学基金(2010GZS0176)。

摘　　要：首先在局部凸的Hausdorff拓扑向量空间引进了带约束的ε-强有效点集的概念,然后在可行域为弧连通的紧集,目标函数为K-弧连通的集值映射情况下,证明了ε-强有效点集非空并得到了带约束的ε-强有效点集的连通性。In this paper,we firstly introduce the concept ofε-strongly effective point set with constraint in locally convex Hausdorff topological vector space.Then,under the conditions that the feasible region is arcwise connected and compact,and the objective function is k-arcwise connected set-valued mapping,we prove theε-stronglyeffective point set is nonempty,and obtain the connectedness ofε-strongly efficient solution set with constraints.

关 键 词：ε-强有效解 连通性 集值映射 

分 类 号：O224[理学—运筹学与控制论]