Generalized cone-subconvexlike set-valued maps and applications to vector optimization  

作　　者：黄永伟 HUANG Yongwei 

机构地区：[1]InstituteofAppliedMathematics,ChongqingUniversity,Chongqing400045,P.R.China [2]DepartmentofSystemsEngineering&EngineeringManagement,TheChineseUniversityofHongKong,HongKong

出　　处：《Journal of Chongqing University》2002年第2期67-71,共5页重庆大学学报（英文版）

摘　　要：The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.

关 键 词：relative interiors generalized cone-subconvexlikeness set-valued vector optimization optimality conditions weak E-minimizer. 

分 类 号：O224[理学—运筹学与控制论]