向量平衡问题解集的稳定性

发布时间：2018-04-25 01:05

本文选题：向量平衡问题 + 向量变分不等式问题　；参考：《广西师范大学》2017年硕士论文

【摘要】：向量平衡问题是非线性泛函分析中重要的分支,在交通运输、金融工程、人力资源等领域有广泛的应用.本文主要研究两类问题:向量平衡问题和向量变分不等式问题解集的稳定性.本论文总共分为四章,具体内容如下:第一章,介绍向量平衡问题和向量变分不等式问题解集稳定性的历史背景和研究现状,同时介绍本文要用到的一些常用符号、基本概念和引理.第二章,在自反Banach空间中研究向量平衡问题解集的弱上半连续性.首先,当约束集和映射同时被不同的参数扰动时,利用向量平衡问题的间隙函数将向量平衡问题转化为凸优化问题,证明向量平衡问题解集的弱上半连续性.其次,我们将混合向量变分不等式问题转化为平衡问题,利用向量平衡问题解集的稳定性结果得到混合向量变分不等式解集的稳定性.第三章,在自反Banach空间中研究向量变分不等式解集的稳定性.当约束集和映射同时被不同的参数扰动时,分别研究当J-goF和F为紧上半连续映射时,向量变分不等式解集的弱上半连续性、闭性.第四章,在Rn空间中,在约束集和映射同时被不同参数扰动时,利用向量变分不等式的拓扑度,得到向量变分不等式解集的下半连续性.与已经获得的结果相比,我们不需要映射满足任何单调性或者严格单调性条件,同时,也不需要任何紧性条件.
[Abstract]:Vector balance problem is an important branch of nonlinear functional analysis, which is widely used in transportation, financial engineering, human resources and other fields. In this paper, we study the stability of solution sets for two kinds of problems: vector equilibrium problem and vector variational inequality problem. This paper is divided into four chapters. The main contents are as follows: the first chapter introduces the historical background and research status of the stability of vector equilibrium problem and vector variational inequality problem, and introduces some commonly used symbols in this paper. Basic concepts and Lemma. In chapter 2, we study the weak upper semicontinuity of solutions for vector equilibrium problems in reflexive Banach spaces. Firstly, when the constraint set and the mapping are disturbed by different parameters simultaneously, the vector equilibrium problem is transformed into a convex optimization problem by using the gap function of the vector equilibrium problem, and the weak upper semi-continuity of the solution set of the vector equilibrium problem is proved. Secondly, we transform the mixed vector variational inequality problem into a equilibrium problem, and obtain the stability of the solution set of mixed vector variational inequality by using the stability result of the solution set of vector equilibrium problem. In chapter 3, we study the stability of the solution set of vector variational inequalities in reflexive Banach spaces. When the constrained set and the mapping are disturbed by different parameters at the same time, the weak upper semicontinuity and closeness of the solution set of vector variational inequalities are studied respectively when J-goF and F are compact upper semicontinuous mappings. In chapter 4, when the constrained set and mapping are disturbed by different parameters at the same time in rn space, the lower half continuity of the solution set of vector variational inequality is obtained by using the topological degree of vector variational inequality. Compared with the obtained results, we do not need the mapping to satisfy any monotonicity or strict monotonicity condition, nor any compactness condition.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224

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