Stampacchia广义向量拟均衡问题Ⅱ

通过引进锥对角拟凸概念,讨论了Stampacchia广义向量拟均衡问题解的存在性.由于该问题包含了许多形式的变分不等式与均衡问题作为特例,所得解的存在性结果推广和发展了近期的一些研究结果,主要有以下两个方面: 1)放宽了对连续性的要求;2)由数值型推广到了向量型.     

Stampacchia 广义向量拟均衡问题II

通过引进锥对角拟凸概念, 讨论了Stampacchia 广义向量拟均衡问题解的存在性.由于该问题包含了许多形式的变分不等式与均衡问题作为特例,所得解的存在性结果推广和发展了近期的一些研究结果,主要有以下两个方面: 1)放宽了对连续性的要求; 2)由数值型推广到了向量型.     

对称向量拟均衡问题与鞍点

提出一类新的对称向量拟均衡问题，证明其解的存在定理，并得到向量鞍点定理．本文是作者相关工作的继续．     

一种新的向量互补问题

本文在实局部凸空间中引入了一种新的向量互补问题,这一向量互补问题不仅包含了由Ｙｕ和Ｙａｏ提出的广义向量互补问题由Ｃｈｅｎ和Ｙａｎｇ定义的弱向量互补问题,而且还包含了Ｉｓａｃ意义下的隐互补问题。本文还讨论了新的向量互补问题,向量变分不等式,向量单向极小化问题和最小元问题之间的关系,给出了这一向量互补问题解的存在定理。     

一类新型的广义向量拟均衡问题

提出一类新的广义向量拟均衡问题，并得到解的存在性定理．用于证明向量变分不等式和向量优化问题的解的存在性．     

应用向量解决平面几何问题

向量是形与数的高度统一，它集几何图形的直观与代数运算的简洁于一身，在解决平面几何问题中有着奇特的功效．利用向量法解答平面几何问题的一般步骤是：1)将题设和结论中的有关元素转化为向量形式；2)确定必要的基底向量，并用基底表示其他向量；3)借助于向量的运算解决问题。     

利用向量法巧解立体几何中的探索性问题

立体几何中的探索性问题是近年高考命题的一个新的亮点，它侧重考查学生观察发现、类比转化以及运用数学知识分析和解决数学问题的能力．利用空间向量的有关知识，可以有效解决这类问题，它无须进行复杂繁难的作图、论证、推理，只须通过坐标或向量运算进行判断．在解题过程中，往往把“是否存在”问题转化为“点的坐标是否有解”、     

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.     

用空间向量解立体几何题

用传统的综合推理法解立体几何问题往往需要较强的空间想象力，在解决角度、距离问题时技巧性较强，一旦思路受阻就只能放弃．新课程增加的空间向量利用代数的方法，为解决这些问题提供了通用方法．其显著优点是减弱了推理论证的成份，用计算来代替论证，其缺点是计算量加大．如果在解决问题的过程中推理论证与向量运算综合运用，则不失为一种好办法!     

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.     

Stampacchia Generalized Vector Quasiequilibrium Problems and Vector Saddle Points

In this paper, Stampacchia generalized vector quasiequilibrium problem and generalized vector loose saddle points for set-valued mappings are introduced. By using the scalarization method and the fixed-point theorem, existence theorems are established.This work was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China. The author is grateful to Professor F. Giannessi and the referee for valuable comments and careful reading improving the original draft.Communicated by F. Giannessi     

Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems

In this paper, we study the relationship among the generalized Minty vector variational-like inequality problem, generalized Stampacchia vector variational-like inequality problem and vector optimization problem for nondifferentiable and nonconvex functions. We also consider the weak formulations of the generalized Minty vector variational-like inequality problem and generalized Stampacchia vector variational-like inequality problem and give some relationships between the solutions of these problems and a weak efficient solution of the vector optimization problem.     

On vector variational-like inequalities and vector optimization problems with (G,α)-invexity

The aim of this paper is to study the relationship among Minty vector variationallike inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving(G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem,Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of(G, α)-invex functions. Examples are provided to elucidate our results.     

On Nondifferentiable and Nonconvex Vector Optimization Problems

In this paper, we prove the equivalence among the Minty vector variational-like inequality, Stampacchia vector variational-like inequality, and a nondifferentiable and nonconvex vector optimization problem. By using a fixed-point theorem, we establish also an existence theorem for generalized weakly efficient solutions to the vector optimization problem for nondifferentiable and nonconvex functions.     

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.     

Vector variational inequalities on Hadamard manifolds involving strongly geodesic convex functions

This paper is intended to study the vector variational inequalities on Hadamard manifolds. Generalized Minty and Stampacchia vector variational inequalities are introduced involving generalized subdifferential. Under strongly geodesic convexity, relations between solutions of these inequalities and a nonsmooth vector optimization problem are established. To illustrate the relationship between a solution of generalized weak Stampacchia vector variational inequality and weak efficiency of a nonsmooth vector optimization problem, a non-trivial example is presented.     

Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency

In this paper, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Here, a generalized Stampacchia vector variational inequality is formulated as a tool to characterize quasi- or weak quasi-efficient points. By using two new classes of generalized convexity functions, under suitable constraint qualifications, the equivalence between Kuhn–Tucker vector critical points, solutions to the multiobjective problem and solutions to the generalized Stampacchia vector variational inequality in both weak and strong forms will be proved.     

Vector variational inequality with pseudoconvexity on Hadamard manifolds

In this paper, we give some properties for nondifferentiable pseudoconvex functions on Hadamard manifolds, and discuss the connections between pseudoconvex functions and pseudomonotone vector fields. Moreover, we study Minty and Stampacchia vector variational inequalities, which are formulated in terms of Clarke subdifferential for nonsmooth functions. Some relations between the vector variational inequalities and nonsmooth vector optimization problems are established under pseudoconvexity or pseudomonotonicity. The results presented in this paper extend some corresponding known results given in the literatures.     

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.