The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperatio...The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperation theorem, Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions, the necessary conditions are obtained for the set-valued optimization problem to attain its super efficient solutions. Also, the sufficient conditions for Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions are derived.展开更多
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
The existence conditions of globally proper efficient points and a useful property of ic- cone-convexlike set-valued maps are obtained. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for...The existence conditions of globally proper efficient points and a useful property of ic- cone-convexlike set-valued maps are obtained. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for globally proper efficient solutions are established in terms of Lagrange multipliers. The new concept of globally proper saddle-point for an appropriate set-valued Lagrange map is introduced and used to characterize the globally proper efficient solutions. The results which are obtained in this paper are proven under the conditions that the ordering cone need not to have a nonempty interior.展开更多
基金Supported by the National Natural Science Foundation of China (10461007)the Science and Technology Foundation of the Education Department of Jiangxi Province (GJJ09069)
文摘The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperation theorem, Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions, the necessary conditions are obtained for the set-valued optimization problem to attain its super efficient solutions. Also, the sufficient conditions for Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions are derived.
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.
基金Supported by Natural Science Foundation of Ningxia (No.NZ0959)Natural Science Foundation of the State Ethnic Affairs Commission of PRC (No.09BF06)Natural Science Foundation for the Youth (No.10901004)
文摘The existence conditions of globally proper efficient points and a useful property of ic- cone-convexlike set-valued maps are obtained. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for globally proper efficient solutions are established in terms of Lagrange multipliers. The new concept of globally proper saddle-point for an appropriate set-valued Lagrange map is introduced and used to characterize the globally proper efficient solutions. The results which are obtained in this paper are proven under the conditions that the ordering cone need not to have a nonempty interior.
