某些变分不等式的间隙函数、误差界和算法研究
发布时间：2018-09-03 06:17
【摘要】：摘要:本论文主要研究了集值拟变分不等式问题的间隙函数和误差界,集值混合变分不等式问题的投影算法.全文共分三个章节,具体内容如下:第一章,分别介绍了本文的研究背景、现状及主要内容.第二章,首先研究了集值拟变分不等式的间隙函数,然后利用该间隙函数建立了集值拟变分不等式与优化问题间的等价关系.最后,通过这一等价关系讨论了集值拟变分不等式的误差界问题.第三章,提出了一种集值混合变分不等式新的投影算法.在迭代的每一步,首先利用当前点xi,通过计算预解算子得到点zi,其中的迭代步长满足某种Armjo线搜索.然后,利用zi构造出分离当前点xi及集值混合变分不等式解集的超平面,再将当前点向该超平面做投影得到下一步迭代点.在一定的条件下,给出了该算法产生的无穷序列具有全局收敛性.最后,给出了算法的数值计算结果.
[Abstract]:Absrtact: in this paper, the gap function and error bound for set-valued quasi-variational inequality problems and the projection algorithm for set-valued mixed variational inequality problems are studied. This paper is divided into three chapters. The main contents are as follows: the first chapter introduces the research background, current situation and main contents of this paper. In the second chapter, the gap function of set-valued quasi variational inequality is studied, and then the equivalent relation between the set valued quasi variational inequality and the optimization problem is established by using the gap function. Finally, the error bound problem of set-valued quasi variational inequalities is discussed by using this equivalence relation. In chapter 3, a new projection algorithm for set-valued mixed variational inequalities is proposed. In each step of the iteration, the point zi, is obtained by calculating the resolvent operator using the current point xi,. The iteration step size satisfies some Armjo line search. Then, using zi to construct the hyperplane that separates the current point xi and the solution set of the set-valued mixed variational inequality, and then projecting the current point to the hyperplane to get the next iteration point. Under certain conditions, the global convergence of the infinite sequence generated by the algorithm is given. Finally, the numerical results of the algorithm are given.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O178
本文编号：2219138
[Abstract]:Absrtact: in this paper, the gap function and error bound for set-valued quasi-variational inequality problems and the projection algorithm for set-valued mixed variational inequality problems are studied. This paper is divided into three chapters. The main contents are as follows: the first chapter introduces the research background, current situation and main contents of this paper. In the second chapter, the gap function of set-valued quasi variational inequality is studied, and then the equivalent relation between the set valued quasi variational inequality and the optimization problem is established by using the gap function. Finally, the error bound problem of set-valued quasi variational inequalities is discussed by using this equivalence relation. In chapter 3, a new projection algorithm for set-valued mixed variational inequalities is proposed. In each step of the iteration, the point zi, is obtained by calculating the resolvent operator using the current point xi,. The iteration step size satisfies some Armjo line search. Then, using zi to construct the hyperplane that separates the current point xi and the solution set of the set-valued mixed variational inequality, and then projecting the current point to the hyperplane to get the next iteration point. Under certain conditions, the global convergence of the infinite sequence generated by the algorithm is given. Finally, the numerical results of the algorithm are given.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O178
【参考文献】
相关期刊论文 前3条
1 涂凯;夏福全;;A PROJECTION-TYPE ALGORITHM FOR SOLVING GENERALIZED MIXED VARIATIONAL INEQUALITIES[J];Acta Mathematica Scientia(English Series);2016年06期
2 夏福全;黎小波;;Banach空间中分离变分不等式的Levitin-Polyak-α适定性(英文)[J];四川师范大学学报(自然科学版);2012年03期
3 何诣然;;一个关于混合变分不等式问题的投影算法[J];数学物理学报;2007年02期
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