An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict effi...An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict efficient solution are derived, respectively.展开更多
In this paper, the strictly weak major efficient point of set is introduced. A functional as a separate function is constructed, therefore, a necessary and sufficient condition for the strictly weak major efficient po...In this paper, the strictly weak major efficient point of set is introduced. A functional as a separate function is constructed, therefore, a necessary and sufficient condition for the strictly weak major efficient point of set is established.展开更多
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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China(10461007)Supported by the Natural Science Foundation of Jiangxi Province(0611081)
文摘An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict efficient solution are derived, respectively.
文摘In this paper, the strictly weak major efficient point of set is introduced. A functional as a separate function is constructed, therefore, a necessary and sufficient condition for the strictly weak major efficient point of set is established.
基金This research was supported by the National Natural Science Foundation of China Grant(11961047)the Natural Science Foundation of Jiangxi Province(20192BAB201010).
文摘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.
