含参集值向量均衡问题各种有效解映射的下半连续性

在实Hausdorff拓扑向量空间中,引进含参集值向量均衡问题,给出各种有效解的概念.在锥-次类凸的条件下,得到各种有效解的标量化结果.结合集值映射的弱f-性,在适当假设条件下,得到含参集值向量均衡问题各种有效解映射的下半连续性.     

集值广义强向量拟均衡问题解的存在性

利用集值映射的自然拟C-凸性和集值映射的下(-C)-连续性的定义以及Kakutani-Fan-Glicksberg不动点定理,在不要求锥C的对偶锥C~*具有弱*紧基的情况下,建立了集值广义强向量拟均衡问题解的存在性定理.把相关文献中所得的关于单值映射解的存在性结果推广到了集值映射的情形.     

集值映射的对称向量拟均衡问题

研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理.     

含参广义集值向量均衡问题有效解映射下半连续的最优条件

在实Hausdorff拓扑向量空间中研究一类含参广义集值向量均衡问题弱有效解与有效解映射的下半连续性. 在近似锥-次类凸的条件下, 运用标量化的方法得到弱有效解的标量化结果. 在适当条件下, 得到含参广义集值向量均衡问题弱有效解与有效解映射下半连续性定理.     

集值映射向量优化问题的锥弱有效解的镇定性和稳定性

本文研究了集值映射向量优化问题的锥弱有效解的镇定性和稳定性,我们引进了集值映射向量优化问题的镇定性和稳定性的定义,并证明了集值映射问题优化问题的镇定性和稳定性的一些主要定理。     

一类集值映射的向量均衡问题

在拓扑向量空间内,研究了一类新的集值映射的广义向量均衡问题,利用KKM定理,证明了解的几个存在性定理,并讨论了解的性状.所得结果推广了近期一些作者的研究成果.     

偏序线性空间中向量集值映射最优化问题解的鞍点条件和Lagrange对偶

本文在没有任何拓扑结构的条件下，给出了向量集值映射最优化问题解的鞍点充分和必要条件以及Ｌａｇｒａｎｇｅ对偶，从而将文献（１）中的有关结果推广到更一般的偏序线性空间，并进一步给出了逆对偶定理。     

一类隐式集值向量均衡问题解的存在性和解集的稳定性

研究一类隐式集值向量均衡问题,它是隐式向量均衡问题、隐式变分不等式问题、隐式相补问题、向量均衡问题和向量变分不等式问题等的推广.利用截口定理,在Hausdorff拓扑线性空间的非紧子集上得出了一些隐式集值向量均衡问题解的存在性结果.并且还讨论了该隐式集值向量均衡问题解集的通有稳定性.这些结果推广和统一了近期的一些相关结果.     

集值均衡与Browder变分包含问题解的存在性

本文利用Ky Fan引理,研究在锥情形下集值均衡问题解的存在性,推广了近期文献中的相关结果,并在锥形式下,讨论Browder变分包含问题.     

集值映射向量优化问题的e-真有效解

引入了集值映射向量优化问题的αe-弱有效解、e-真有效解、e-真鞍点概念,在近似广义C-次似凸条件下,建立了e-真有效解的标量化定理、Lagrang乘子定理和e-真鞍点定理,并讨论了集值映射向量优化问题的αe-弱有效解的标量化定理和Laugrange乘子定理,推广了已有结果。     

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．     

Characterizations of Solutions for Vector Equilibrium Problems

In this paper, we characterize the solutions of vector equilibrium problems as well as dual vector equilibrium problems. We establish also vector optimization problem formulations of set-valued maps for vector equilibrium problems and dual vector equilibrium problems, which include vector variational inequality problems and vector complementarity problems. The set-valued maps involved in our formulations depend on the data of the vector equilibrium problems, but not on their solution sets. We prove also that the solution sets of our vector optimization problems of set-valued maps contain or coincide with the solution sets of the vector equilibrium problems.     

Existence of a Solution and Variational Principles for Vector Equilibrium Problems

In this paper, we prove an existence result for a solution to the vector equilibrium problems. Then, we establish variational principles, that is, vector optimization formulations of set-valued maps for vector equilibrium problems. A perturbation function     

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.     

隐式形式多值向量均衡问题解的存在性

考虑一类隐式形式多值向量均衡问题的解的存在性,该类问题包含了多值均衡问题、隐式向量均衡问题、多值变分不等式问题、向量变分不等式问题以及向量互补问题作为其特殊情形.利用广义Fan-Browder不动点定理,得到了拓扑向量空间中该类问题解的存要性定理,该结果推广并统一了已有问题解的存在性结果.     

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.     

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．     

Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems

In this paper, a gap function for a system of vector equilibrium problems is introduced and studied. Some necessary and sufficient conditions for the system of vector equilibrium problems are established. Characterizations of the solutions set for the system of vector equilibrium problems are also derived. Furthermore, some existence results of solutions for the system of vector equilibrium problems are proved. This work was supported by the National Natural Science Foundation of China, the Youth Foundation, Sichuan Education Department of China, the National Natural Science Foundation, Sichuan Education Department of China (2004C018), and a grant from the National Science Council of ROC.     

Existence of Solutions to Generalized Vector Quasi-variational-like Inequalities with Set-valued Mappings

In this paper, we introduce and study a class of generalized vector quasivariational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.