Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikene...Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikeness, some characterizations of the super efficiency are given in terms of scalarization and Lagrangian multipliers. Related results are generalized.展开更多
Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearl...Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.展开更多
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 bet...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.展开更多
In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is establis...In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function.展开更多
In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under ...In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.展开更多
Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applyin...Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.展开更多
In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,u...In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.展开更多
In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. ...In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. A new duality form is introducedand the duality theorems are 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
文摘Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikeness, some characterizations of the super efficiency are given in terms of scalarization and Lagrangian multipliers. Related results are generalized.
文摘Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.
文摘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.
基金the Natural Science Foundation of Zhejiang Province,China(M103089)
文摘In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function.
基金Foundation item： Supported by the Natural Science Foundation of China（10871216） Supported by the Natural Science Foundation Project of CQ CSTC（2008BB0346, 2007BB0441） Supported by the Excellent Young Teachers Program of Chongqing Jiaotong University（EYT08-016） Acknowledgement The author would like to thank the anonymous referee for the valuable remarks that helped considerably to correct and to improve the presentation.
文摘In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.
基金Supported by the National Natural Science Foundation of China (10571035,10871141)
文摘Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.
基金Supported by the Natural Science Foundation of the Education Department of Henan Province（2004110008）
文摘In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.
文摘In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. A new duality form is introducedand the duality theorems are 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.
