Optimality Conditions for D.C. Vector Optimization Problems Under Reverse Convex Constraints

In this paper, we establish global necessary and sufficient optimality conditions for D.C. vector optimization problems under reverse convex constraints. An application to vector fractional mathematical programming is also given. Mathematics Subject Classifications (1991). Primary 90C29, Secondary 49K30.     

拓扑向量空间中的几个锥广义凸映射

本文引进拓扑向量空间中的几个锥伪凸映射的概念,并且讨论了它们之间及其它的锥广义凸映射之间的关系,最后,给出一个显示各种关系的图表。     

向量优化问题广义有效点的一个存在性定理

利用集值映射不动点定理及最优化问题与变分不等式的关系给出线性G^↑ateaux可微的锥凸映射的广义有效点的一个存在性定理。     

映射系统中的零序列

设（Ｅ，ｒ）是局部凸拓扑向量空间，Ω是任意抽象集合，Ｆ∈Ｅ＾Ω，（ｘｊ）∈Ω是映射系统（Ω，Ｆ）中的零序列，即对每个ｆ∈Ｆ，（ｆ（ｘｊ））都是（Ｅ，τ）中收敛于０的序列，本文给出了序列（ｆ（ｘｊ））的Ｆ的子集Ｂ上一致收敛于０的刻划。     

Vector Equilibrium Problems. Existence Theorems and Convexity of Solution Set

The natural quasi-concavity of set-valued mappings in an ordered vector space is introduced. Existence theorems for vector equilibrium problems involving set-valued monotone mappings are obtained and the convexity of the solution set is shown.     

THE OPTIMALITY CONDITIONS OF NONCONVEXSET-VALUED VECTOR OPTIMIZATION

1 IntroductionIt is well known that the most linportant task of nonsmooth is to extend the classicaIderivatives to broaden tl1e scope of dtherentiable function. One of the importallt geuerallzationis the Clarke's generalized directional derivative[1]--[2]…     

A Fixed Point Theorem and Some Generalized Ky Fan's Minimax Inequalities

In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without "local convexity". And we also establish some generalized Ky Fan's minimax inequalities for set-value vector mappings, which are the generalization of some previous results.     

向量均衡问题

本首先引进了集值映射的伪单调性，利用Ky Fan引理以及KKM映射对一般向量均衡问题建立了相应的存在性定理．     

广义向量似变分不等式解集的通有稳定性

本文首先得到广义向量似变分不等式问题的解的存在性定理,然后利用UＳＣＯ映射的性质（见ＴａｎＫＫ（ｅｔａｌ）（１９９５））,讨论广义向量似变分不等式的解集的通有稳定性,得到大多数（拓扑意义下）广义向量似变分不等式问题的解集是稳定的．     

向量似变分不等式解的存在性及解集的稳定性

本文首先得到一类广义向量似变分不等式问题的解的存在性定理,然后利用usco映射的性质,讨论广义向量似变分不等式的解集的通有稳定性,得到大多数(在Baire分类意义下)广义向量似变分不等式问题的解集是稳定的;另外还引入广义向量似变分不等式解集的本质连通区的概念,并证明了满足一定连续性、凸性条件的广义向量似变分不等式的解集至少存在一个本质连通区.     

集值映射最优化问题超有效解集的连通性

本文在局部凸空间中对集值映射最优化问题引入超有效解的概念．首先研究了超 有效点的一些重要特性．其后证明了当目标函数为锥类凸的集值映射时，其目标空间里 的超有效点集是连通的；若目标函数为锥凸的集值映射时，其超有效解集也是连通的．     

On Optimality Condition for Vector Optimization Based on Convex Set-Valued Mapping

1.IntroductionTheoptimalityconditionsofmathematicalprogrammingisaveryimportantsubjectbecausetLeyprovideausefulanalyticaltoolforstudingthedualitytheoryandnonlinearprogrammingalgoirthms.Inrecelltyears,someauthorshavebeguntostudytheoptimalityconditionsforvectoroptimizationproblemofset-valuedmapping,suchas[4][51.Inthispaperlwedefinetheconceptofcone--weaklyefficientsubdifferentialofset-valuedmappinginthecaseofgeneralpartiallyorderedlocallyconvextopologicalvectorspaces.Thecone-weaklysubdifferential…     

THE EXISTENCE THEOREM OF THE CONE-WEAK SUBDIFFERENTIAL OF SET-VALUED MAPPING

In this paper, the existence theorem of the cone-weak subdiflerential of set-valued mapping in locally convex topological vector space is proved.     

关于一类Fuzzy映射的广义变分不等式

本文在拓扩向量空间中研究一类Fuzzy映射的广义变分不等式问题,讨论了这类变分不等式解集的性质及满射性。本文结果改进、推广了作者在[1,2]中的相应结果。     

SYSTEM OF GENERALIZED VECTOR VARIATIONAL INEQUALITIES

1IntroductionA vector variational inequality(for short,VVI),as an important generalization of the clas-sical variational inequality,was first introduced and studied by Giannessi[6]in finite dimensionalEuclidean spaces.Later on,a VVI was studied and genera…     

Mappings preserving spectrum and commutativity on Hermitian matrices

The general form of a continuous mapping φ acting on the real vector space of all n × n complex Hermitian or real symmetric matrices, and preserving spectrum and commutativity, is derived. It turns out that φ is either linear or its image forms a commutative set.     

向量优化问题的对偶性(英文)

Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.     

FC-空间内的广义向量变分型不等式

在FC-空间中引入和研究了一类广义向量变分型不等式(GVVTIP),包含了大多数向量平衡问题,向量变分不等式问题,广义向量平衡问题和广义向量变分不等式问题作为特殊情况．利用F-KKM定理,在非紧FC-空间中,建立了关于GVVTIP解的某些新的存在定理．这些定理统一、改进和推广了文献中的一些重要的已知结果．     

Minty lemma for inverted vector variational inequalities

In this paper, we introduce Stampacchia-type inverted vector variational inequalities and Minty-type inverted vector variational inequalities and discuss Minty lemma for the inequalities showing the existence of solutions to them in Banach spaces. Next, we consider the equivalence of our Minty lemma with Brouwer’s fixed point theorem as an application.