有限多个变分不等式的一般迭代法及在优化中的应用
发布时间：2018-08-27 05:44
【摘要】：本文在实Hilbert空间中引入了某个优化问题的一般迭代法,此优化问题的约束集是关于连续单调映像的有限多个变分不等式问题的解集、有限多个变分包含问题的解集和一个连续伪压缩映像的不动点集之交集.本文主要分为四部分,下面我们逐一来介绍.第一章,主要介绍了变分不等式理论的研究简况和本文的主要工作.第二章,给出了所建议的隐式迭代算法及其性质.第三章,在适当的控制条件下,依据隐式迭代法的性质,证明了该方法强收敛到交集中的一个元,该元是某个优化问题的唯一解.由此即得,该方法强收敛到交集中唯一的范数最小元.第四章,介绍了同样也能够建立显式迭代法,并给出了显式迭代法的收敛性分析结果.本文结果是对已有结果的改进和推广.
[Abstract]:In this paper, we introduce a general iterative method for an optimization problem in real Hilbert spaces. The constrained set of the optimization problem is the solution set of finite variational inequalities for continuous monotone mapping. The intersection of the solution set of finite variational inclusions and the fixed point set of a continuous pseudo contractive mapping. This article is mainly divided into four parts, below we introduce one by one. In the first chapter, the research situation of variational inequality theory and the main work of this paper are introduced. In chapter 2, the proposed implicit iterative algorithm and its properties are given. In chapter 3, under appropriate control conditions, according to the properties of implicit iterative method, it is proved that the method converges strongly to an element in the intersection, which is the unique solution of an optimization problem. It is obtained that the method converges strongly to the unique norm minimum element in the intersection. In chapter 4, the explicit iterative method is also introduced, and the convergence analysis results of the explicit iterative method are given. The results in this paper improve and generalize the existing results.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.91
本文编号：2206260
[Abstract]:In this paper, we introduce a general iterative method for an optimization problem in real Hilbert spaces. The constrained set of the optimization problem is the solution set of finite variational inequalities for continuous monotone mapping. The intersection of the solution set of finite variational inclusions and the fixed point set of a continuous pseudo contractive mapping. This article is mainly divided into four parts, below we introduce one by one. In the first chapter, the research situation of variational inequality theory and the main work of this paper are introduced. In chapter 2, the proposed implicit iterative algorithm and its properties are given. In chapter 3, under appropriate control conditions, according to the properties of implicit iterative method, it is proved that the method converges strongly to an element in the intersection, which is the unique solution of an optimization problem. It is obtained that the method converges strongly to the unique norm minimum element in the intersection. In chapter 4, the explicit iterative method is also introduced, and the convergence analysis results of the explicit iterative method are given. The results in this paper improve and generalize the existing results.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.91
【参考文献】
相关期刊论文 前1条
1 张石生;李向荣;陈志坚;;Algorithms of common solutions to quasi variational inclusion and fixed point problems[J];Applied Mathematics and Mechanics(English Edition);2008年05期
，本文编号：2206260
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