含参数集值向量优化问题强有效点集的连通性  

The Connectedness of Strong Effective Point Set for Set-valued Vector Optimization Problems with Parameters

作　　者：赖遵远 陈剑尘[1] 刘富荣 LAI Zun-yuan;CHEN Jian-chen;LIU Fu-rong(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,江西南昌330063

出　　处：《数学的实践与认识》2021年第21期242-249,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11061023);江西省自然科学基金(2010GZS0176);南昌航空大学研究生创新专项(YC2019037)。

摘　　要：在Hausdorff局部凸的拓扑线性空间中,给出了含参数的强有效点集的概念.研究了在含参数的目标集值映射为锥弧连通的,可行域为弧连通紧的,参数是扰动的情况下含参数的强有效点集的连通性.在适当的条件下,得到了含参数集值向量优化问题强有效点集的连通性定理.In this paper,we give the concept of strong effective point set with parameters in the Hausdorff locally convex topological linear space.The connectedness of the strong effective point set with parameters is researched when the objective set-valued map with parameters is cone-arcwise connected,the feasible region is arcwise connected and compact,and the parameters are perturbed.Under suitable conditions,a connectedness theorem of strong effective point sets for the set-valued vector optimization problem with parameters is obt ained.

关 键 词：集值向量优化 含参强有效点 C-弧连通 连通性 

分 类 号：O224[理学—运筹学与控制论]