一个关于混合变分不等式问题的投影算法

数学物理学报

一个关于混合变分不等式问题的投影算法

何诣然

四川师范大学数学与软件科学学院成都 610068

收稿日期:2005-10-20 修回日期:2006-06-06 出版日期:2007-04-25 发布日期:2007-04-25
通讯作者: 何诣然
基金资助:
国家自然科学基金(A0324638)、四川省科技厅青年基金(06ZQ026-013)和四川省基础数学重点学科基金(SZD0406)资助

A New Projection Algorithm for Mixed Variational Inequalities

He Yiran

Department of Mathematics, Sichuan Normal University, Chengdu 610068

Received:2005-10-20 Revised:2006-06-06 Online:2007-04-25 Published:2007-04-25
Contact: He Yiran

摘要/Abstract

摘要： 作者提出了混合变分不等式的一个新的投影算法. 混合变分不等式在弹性塑料学领域有实际应用, 而且形式上比经典的变分不等式更一般. 假设映射具有某种伪单调性, 作者证明了所提出的新算法是全局收敛的. 如果某种误差届成立, 算法的收敛率也被分析.

关键词: 混合变分不等式, 投射算法, 弹性塑料学, 伪单调

Abstract: A new projection algorithm is proposed for mixed variational inequalities. Mixed variational inequalities are more general than classical variational inequalities and have rather practical applications in elastoplastic problems. Assuming that the underlying mapping F is pseudo-monotone with respect
to the underlying function $\varphi$, the author proves that this new method is globally convergent. In addition, when a certain error bound holds locally, the author analyzes the convergence rate of the iteration sequence.

Key words: Mixed variational inequalities, Projection algorithm, Elastoplastic problems, Pseudomonotone

中图分类号:

90C33

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, 27(2): 215-220.

He Yiran. A New Projection Algorithm for Mixed Variational Inequalities[J]. Acta mathematica scientia,Series A, 2007, 27(2): 215-220.

[1]	魏利, Agarwal Ravi P. 含有广义p-Laplacian算子的双曲型非线性微分方程的单调性方法[J]. 数学物理学报, 2015, 35(5): 867-877.
[2]	朱莉, 夏福全. 广义混合变分不等式的Levitin-Polyak适定性[J]. 数学物理学报, 2012, 32(4): 633-643.
[3]	范丽亚, 刘三阳. 二层规划可行解的存在性[J]. 数学物理学报, 2003, 23(6): 739-744.