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
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.
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.
