Optimality Conditions for Strictly Efficient Solutions in Set-valued Optimization  

作　　者：Yi-hong XU 

机构地区：[1]Department of Mathematics,School of Sciences,Nanchang University,Nanchang 330031,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第4期891-901,共11页应用数学学报（英文版）

基　　金：This research was supported by the National Natural Science Foundation of China Grant(11961047);the Natural Science Foundation of Jiangxi Province(20192BAB201010).

摘　　要：A new kind of tangent derivative,M-derivative,for set-valued function is introduced with help of a modified Dubovitskij-Miljutin cone.Several generalized pseudoconvex set-valued functions are introduced.When both the objective function and constraint function are M-derivative,under the assumption of near conesubconvexlikeness,by applying properties of the set of strictly efficient points and a separation theorem for convex sets,Fritz John and Kuhn-Tucker necessary optimality conditions are obtained for a point pair to be a strictly efficient element of set-valued optimization problem.Under the assumption of generalized pseudoconvexity,a Kuhn-Tucker sufficient optimality condition is obtained for a point pair to be a strictly efficient element of set-valued optimization problem.

关 键 词：strict efficiency near cone-subconvexlikeness set-valued optimization CONE 

分 类 号：O224[理学—运筹学与控制论]