On Generalized Vector Equilibrium Problems

A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of the solution sets are established.     

Generalized Vector Equilibrium Problems with Trifunctions

In this paper, we study the existence of strong and weak solutions of the generalized vector equilibrium problems for trifunctions. Two special classes of vector-valued trifunctions are introdcued, called the classes of (SPM) and (GPM), respectively. Some existence results for strong solutions associated to functions of these classes are given.     

Generalized Vector Equilibrium Problems with Trifunctions

In this paper, we study the existence of strong and weak solutions of the generalized vector equilibrium problems for trifunctions. Two special classes of vector-valued trifunctions are introdcued, called the classes of (SPM) and (GPM), respectively. Some existence results for strong solutions associated to functions of these classes are given.     

Generalized Vector Equilibrium Problems in Generalized Convex Spaces

In this paper, we introduce and study a class of abstract generalized vector equilibrium problems (AGVEP) in generalized convex spaces which includes most vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems, and generalized vector variational inequality problems as special cases. By using the generalized GKKM and generalized SKKM type theorems due to the first author, some new existence results of equilibrium points for the AGVEP are established in noncompact generalized convex spaces. As consequences, some recent results in the literature are obtained under much weaker assumptions.     

Vector Equilibrium Problems with Generalized Monotone Bifunctions

A vector equilibrium problem is defined as follows: given a closed convex subset K of a real topological Hausdorff vector space and a bifunction F(x, y) valued in a real ordered locally convex vector space, find x ^*K such that for all yK. This problem generalizes the (scalar) equilibrium problem and the vector variational inequality problem. Extending very recent results for these two special cases, the paper establishes existence of solutions for the unifying model, assuming that F is either a pseudomonotone or quasimonotone bifunction.     

拓扑序空间中的广义向量值均衡问题

利用一个KKM型定理,在拓扑序空间中,建立了关于广义向量值均衡问题解的某些新的存在性定理.     

关于集值目标映射的向量平衡问题的广义Tykhonov适定性

引入集值目标映射的向量平衡问题的两类广义Tykhonov适定性,利用非紧性Kuratowski测度给出它们的度量刻划和讨论这两类适定性的充分性条件.最后证明向量平衡问题的广义Tykhonov适定性与约束极小化问题的广义Tykhonov适定性之间的等价关系.     

FC-空间中含伪单调集值映象的广义向量平衡问题

在FC-空间内引入和研究了几类含伪单调集值映象的广义向量平衡问题．利用第二作者的KKM定理,在FC空间内对这些广义向量平衡问题证明了平衡点的存在性定理,改进与推广了近期文献中的相应结果．     

Semicontinuity of Solution Mappings of Parametric Generalized Vector Equilibrium Problems

In this paper, we study the ε-generalized vector equilibrium problem (ε-GVEP) and the ε-extended vector equilibrium problem (ε-EVEP), which can be regarded as approximate problems to the generalized vector equilibrium problems (GVEP). Existence results for ε-GVEP and ε-EVEP are established. We investigate also the continuity of the solution mappings of ε-GVEP and ε-EVEP. In particular, two results concerning the lower semicontinuity of the solution mappings of ε-GVEP and ε-EVEP are presented. This research was partially supported by Grant NSC 95-2811-M-110-010.     

Semicontinuity of Solution Mappings to Parametric Generalized Vector Equilibrium Problems

In this article, stability results concerning the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mappings to parametric generalized vector equilibrium problems with neither the monotonicity of mappings nor any information of the solution mappings are established by using scalarization methods and a new density result.     

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．     

Generalized Equilibrium Problems and Generalized Complementarity Problems

From a general minimax inequality or an abstract lopsided saddle-point theorem, we deduce general Karamardian-type equilibrium theorems and generalized complementarity theorems. Our new results extend a number of well-known earlier works of many authors.     

Existence Theorems of Simultaneous Equilibrium Problems and Generalized Vector Quasi-Saddle Points

In this paper, we establish the existence theorems of simultaneous equilibrium problems. As consequences of our results, we establish the existence theorem of simultaneous mathematical programs and equilibrium problems and the existence theorems of generalized vector quasi-saddle point problems.     

On Efficiency Conditions for Nonsmooth Vector Equilibrium Problems with Equilibrium Constraints

In this article, necessary conditions of Fritz John type for weak efficient solutions of a nonsmooth vector equilibrium problem involving equilibrium constraints (VEPEC) in terms of the Clarke subdifferentials are established. Under constraint qualifications which are suitable for (VEPEC), necessary conditions of Kuhn-Tucker type for efficiency are derived. Under assumptions on generalized convexity of data, sufficient conditions for efficiency are developed. Some applications to vector variational inequalities and vector optimization problems with equilibrium constraints are also given.     

Stampacchia向量均衡问题与向量相补问题

引进Stampacchia向量均衡问题与一种新的向量相补问题．用数值方法,得到它们的存在定理,并讨论Stampacchia广义向量变分不等式,向量隐相补问题与极小元问题的关系．     

Generalized Nash Equilibrium Problems

The Generalized Nash Equilibrium Problem is an important model that has its roots in the economic sciences but is being fruitfully used in many different fields. In this survey paper we aim at discussing its main properties and solution algorithms, pointing out what could be useful topics for future research in the field.     

Strong Vector Equilibrium Problems

In this paper, the existence of the solution for strong vector equilibrium problems is studied by using the separation theorem for convex sets. The arc-wise connectedness and the closedness of the strong solution set for vector equilibrium problems are discussed; and a necessary and sufficient condition for the strong solution is obtained.     

扰动广义向量平衡问题解集的下半连续性

In this paper,by a scalarization method,the lower semicontinuity of the solution mappings to two kinds of parametric generalized vector equilibrium problems involving set-valued mappings is established under new assumptions which are weaker than the C-strict monotonicity.These results extend the corresponding ones.Some examples are given to illustrate our results.