带约束条件集值优化问题近似Henig有效解集的连通性  

Connectedness of Approximate Henig Efficient Solution Sets for Set-valued Optimization Problems with Constraints

作　　者：吴昌耀 陈剑尘[1] WU Chang-yao;CHEN Jian-chen(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5期221-227,共7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);南昌航空大学博士启动基金(EA200907383);南昌航空大学研究生创新专项(YC2019037);江西省教育厅科技项目(GJJ171544)。

摘　　要：研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理.In this paper,we study the connectedness of the set approximate Henig effective solutions for set-valued optimization problems with constrains.In the real locally convex Hausdorff space,we discuss the existence and connectedness of approximate Henig efficient solution set for the set-valued optimization problems with constraints under the conditions that the feasible region is an arcwise connected and compact subset,and the objective function is C-arc-connected set-valued mapping.The connectedness theorem is given approximate Henig effective solution sets for set-valued optimization problems with constrained.

关 键 词：向量优化 带约束的近似Henig有效解 C-弧连通 连通性 集值映射 

分 类 号：O224[理学—运筹学与控制论]