极大值方程的数值算法及其应用研究
发布时间：2018-11-21 14:18
【摘要】：极大值方程问题是非光滑方程问题中一类很重要的问题,经常被用于求解非线性互补、变分不等式和工程力学等问题,并广泛应用于图像存储、随机均衡及优化控制等问题的研究。本文主要对极大值方程问题的求解算法及其应用进行了研究。第一章对极大值方程问题的相关知识做了简单介绍,其中包括问题的来源、发展情况等,并介绍了极大值方程的应用。第二章给出了求解极大值方程问题的一种参数组合牛顿法,此算法主要借助于一种新的微分形式,在一般的假设条件下,证明了算法的局部超线性收敛结果,最后给出了相关的数值实验表明了算法的有效性。第三章给出了求解极大值方程问题的改进参数组合牛顿法,克服了在算法中要求矩阵kV非奇异的限制,证明了算法的局部超线性收敛性,并给出了相关的数值实验。第四章对一类广义互补问题进行了转化,将其转化为极大值方程问题,并且利用给出的参数组合牛顿法对其进行了求解。
[Abstract]:Maxima equation problem is a very important problem in non-smooth equation problem. It is often used to solve nonlinear complementarity, variational inequality and engineering mechanics, and is widely used in image storage. Study on stochastic equilibrium and optimal control. In this paper, the algorithm and its application of the problem of maximum equation are studied. In the first chapter, we briefly introduce the knowledge about the problem of the maximum equation, including the origin and development of the problem, and introduce the application of the maximum equation. In the second chapter, a parameter combination Newton method is given to solve the maximum value equation problem. This method is mainly based on a new differential form. Under general assumptions, the local superlinear convergence results of the algorithm are proved. Finally, relevant numerical experiments are given to show the effectiveness of the algorithm. In chapter 3, an improved parameter combination Newton method for solving the problem of maximum equation is given, which overcomes the limitation of matrix kV nonsingularity in the algorithm, proves the local superlinear convergence of the algorithm, and gives the relevant numerical experiments. In chapter 4, a class of generalized complementarity problem is transformed into a maximum value equation problem, and it is solved by using the given parameter combination Newton method.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
本文编号：2347220
[Abstract]:Maxima equation problem is a very important problem in non-smooth equation problem. It is often used to solve nonlinear complementarity, variational inequality and engineering mechanics, and is widely used in image storage. Study on stochastic equilibrium and optimal control. In this paper, the algorithm and its application of the problem of maximum equation are studied. In the first chapter, we briefly introduce the knowledge about the problem of the maximum equation, including the origin and development of the problem, and introduce the application of the maximum equation. In the second chapter, a parameter combination Newton method is given to solve the maximum value equation problem. This method is mainly based on a new differential form. Under general assumptions, the local superlinear convergence results of the algorithm are proved. Finally, relevant numerical experiments are given to show the effectiveness of the algorithm. In chapter 3, an improved parameter combination Newton method for solving the problem of maximum equation is given, which overcomes the limitation of matrix kV nonsingularity in the algorithm, proves the local superlinear convergence of the algorithm, and gives the relevant numerical experiments. In chapter 4, a class of generalized complementarity problem is transformed into a maximum value equation problem, and it is solved by using the given parameter combination Newton method.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
【参考文献】
相关期刊论文 前8条
1 朱红焰;岳靖;巩成艳;;非线性互补问题的光滑算法[J];长春理工大学学报(自然科学版);2016年05期
2 宋林森;高岩;;极大值函数Clarke广义Jacobi计算的新算法[J];上海理工大学学报;2016年05期
3 朱红焰;巩成艳;岳靖;;非线性互补问题的光滑牛顿算法[J];阜阳师范学院学报(自然科学版);2016年03期
4 周光辉;张从军;张成虎;王月虎;;非线性互补问题的两种数值解法[J];数学杂志;2016年04期
5 许小芳;马昌凤;;基于一个新的NCP函数的光滑牛顿法求解非线性互补问题[J];数学杂志;2011年04期
6 杜守强;高岩;;求解垂直互补问题的参数牛顿法(英文)[J];运筹学学报;2009年01期
7 ;Nonsmooth Equations of K-T Systems for a Constrained Minimax Problem[J];Journal of Systems Engineering and Electronics;2003年02期
8 常永奎,刘三阳;非线性互补问题的一种不可行非内点连续算法[J];数学研究;2003年01期
，本文编号：2347220
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