|
|||||
|
|
| 求解广义混合单调变分不等式的预解算子方法 | |
| 引用本文： | 孙洪春,孙敏. 求解广义混合单调变分不等式的预解算子方法[J]. 高等学校计算数学学报, 2006, 28(3): 262-271 |
| 作者姓名： | 孙洪春 孙敏 |
| 作者单位： | 1. 临沂师范学院数学系,临沂,276005 2. 枣庄学院数学与信息科学系,枣庄,277160 |
| 摘 要： | 1引言设R~n表示n维欧式空间,‖·‖和＜,＞分别表示R~n中的范数和内积,K为R~n中的非空闭凸集,(?)是R~n到R∪{ ∞)的算子．对于给定的非线性算子T,g：R~n→R~n,考虑下面的广义混合变分不等式,记为GMVI：求u∈R~n满足(Tu)~T(g(v)-g(tu)) (?)(g(v))-(?)(g(u))(?)0,(?)g(v)∈R~n．(1)假如(?)是R~n中非空闭凸集K的指标集,即,(?)(u)≡I_k(u)=(?)．此时GMVI等价于下面的广义变分不等式：求u∈R~n,g(u)∈K满足 |
| 关 键 词： | 预解算子方法 单调变分不等式 混合 广义 求解 非空闭凸集 R^n 欧式空间 |
| 收稿时间： | 2004-11-07 |
| 修稿时间： | 2004-11-07 |
A RESOLVENT OPERATOR METHOD FOR THE GENERAL MIXED MONOTONE VARIATIONAL INEQUALITIES |
|
| Sun Hongchun,Sun Min. A RESOLVENT OPERATOR METHOD FOR THE GENERAL MIXED MONOTONE VARIATIONAL INEQUALITIES[J]. Numerical Mathematics A Journal of Chinese Universities, 2006, 28(3): 262-271 | |
| Authors: | Sun Hongchun Sun Min |
| Abstract: | In this paper,a new resolvent operator method is proposed for the general mixed monotone variational inequalities.The proposed method has the following properties:(i)It adopts a new linear search technique;(ii) It keeps the step- sizes having a uniformly positive bound below.Under the monotonicity of the underlying mapping,the global convergence of the new method is proved. |
| Keywords: | general mixed monotone variational inequalities operator-splitting method resolvent operator maximal monotone operator global convergence |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |