This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved ...This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role.展开更多
The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functi...The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functions are studied. Furthermore, the notion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.展开更多
Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in t...Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in topological vector spaces is dened, and their fundamental properties are presented. The relationships between the cone bounded quasiconvex mapping defined in this paper and cone convex mapping, and other known cone quasiconvex mapping are also discussed.展开更多
In this paper,we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under na...In this paper,we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.展开更多
In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by...In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem.We also present an application of the method to demand theory in economy.展开更多
For the Heisenberg group, we introduce the concept of h-quasiconvex functions. We prove that the notions of h-quasiconvex functions and h-convex set are equivalent and that h-quasiconvex functions are locally bounded ...For the Heisenberg group, we introduce the concept of h-quasiconvex functions. We prove that the notions of h-quasiconvex functions and h-convex set are equivalent and that h-quasiconvex functions are locally bounded from above, and furthermore derive that h-convex functions are locally bounded, therefore it is locally Lipschitz continuous by using recent results by Danielli-Garofalo-Nhieu. Finally we give estimates of the L^∞ norm of the first derivatives of h-quasiconvex functions.展开更多
This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor...This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor multiobjective programming defined by a continuous cone-quasiconvex mapping on a compact convex set ofalternatives.The generalized saddle theorem plays a key role in the proof.展开更多
In this paper,we study the connectedness of proper efficient solution sets of the vector optimization problem for a strict cone--quasiconvex mapping in a separated topological linear space.
In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasico...In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.展开更多
1961年,Ky Fan 将古典的 KKM 定理推广到任意 Hausdorff 拓扑矢量空间,Liu 最近引入了可诱捕和共存概念,在 Hausdorff 拓扑矢量空间内给出了 KKM 原理的一种新的变形及其对 Von Neu-mann 和 Ky Fan 型不等式的应用,得到了一些新结果及...1961年,Ky Fan 将古典的 KKM 定理推广到任意 Hausdorff 拓扑矢量空间,Liu 最近引入了可诱捕和共存概念,在 Hausdorff 拓扑矢量空间内给出了 KKM 原理的一种新的变形及其对 Von Neu-mann 和 Ky Fan 型不等式的应用,得到了一些新结果及已知结果的刻划.本文目的是将 Liu 的主要结果改进和推广到没有线性结构的 H-空间,同时在 H-空间中得到了 Von Neumann 和 Ky Fan 型sup inf sup 形式不等式.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（70071026）
文摘This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role.
基金Supported by the National Natural Science Foundation of China（11074099）
文摘The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functions are studied. Furthermore, the notion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.
基金Supported by the National Natural Science Foundation of China (No.70071026).
文摘Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in topological vector spaces is dened, and their fundamental properties are presented. The relationships between the cone bounded quasiconvex mapping defined in this paper and cone convex mapping, and other known cone quasiconvex mapping are also discussed.
基金Coordenação de Aperfeiçoamento de Pessoal de Nível Superior of the Federal University of Rio de Janeiro(UFRJ),Brazil.
文摘In this paper,we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.
文摘In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem.We also present an application of the method to demand theory in economy.
基金Supportecl in part by SF for Pure Research of Natural Sciences of the Education Department of Hunan Province （No.2004c251）, Natural Science Foundation of Hunan Province （No.05JJ30006） and National Natural Science Foundation of China （No.10471063） and specialized Research Fund for Doctoral Program of Higher Education of China.
文摘For the Heisenberg group, we introduce the concept of h-quasiconvex functions. We prove that the notions of h-quasiconvex functions and h-convex set are equivalent and that h-quasiconvex functions are locally bounded from above, and furthermore derive that h-convex functions are locally bounded, therefore it is locally Lipschitz continuous by using recent results by Danielli-Garofalo-Nhieu. Finally we give estimates of the L^∞ norm of the first derivatives of h-quasiconvex functions.
基金Supported by the National Natural Science Foundation of China (No.70071026)
文摘This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor multiobjective programming defined by a continuous cone-quasiconvex mapping on a compact convex set ofalternatives.The generalized saddle theorem plays a key role in the proof.
文摘In this paper,we study the connectedness of proper efficient solution sets of the vector optimization problem for a strict cone--quasiconvex mapping in a separated topological linear space.
基金supported by the Scientific Research Fun of Sichuan Normal University (09ZDL04)the Sichuan Province Leading Academic Discipline Project (SZD0406)
文摘In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.
文摘1961年,Ky Fan 将古典的 KKM 定理推广到任意 Hausdorff 拓扑矢量空间,Liu 最近引入了可诱捕和共存概念,在 Hausdorff 拓扑矢量空间内给出了 KKM 原理的一种新的变形及其对 Von Neu-mann 和 Ky Fan 型不等式的应用,得到了一些新结果及已知结果的刻划.本文目的是将 Liu 的主要结果改进和推广到没有线性结构的 H-空间,同时在 H-空间中得到了 Von Neumann 和 Ky Fan 型sup inf sup 形式不等式.
