| 求解结构型单调变分不等式的改进的邻近类分解方法 |
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| 引用本文： | 李敏,袁晓明. 求解结构型单调变分不等式的改进的邻近类分解方法[J]. 应用数学和力学, 2007, 28(12): 1483-1492 |
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| 作者姓名： | 李敏 袁晓明 |
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| 作者单位： | 东南大学 经济管理学院 管理科学与工程系,南京 210096;2.上海交通大学, 安泰经济与管理学院 管理科学系,上海 200052 |
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| 基金项目： | 国家自然科学基金;国家高技术研究发展计划(863计划) |
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| 摘 要： | 邻近类分解方法首先是由Chen和Teboulle（Math. Programming,1994,64(1):81-101）提出用来求解凸的极小化问题．在此基础上，该文提出一种新方法求解具有分离结构的单调变分不等式．其主要优点在于放松了算法中对某些参数的限制，使得新方法更加便于计算．在和原分解方法相同的假设下，可以证明新方法是全局收敛的．
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| 关 键 词： | 分解 非精确准则 邻近 结构型变分不等式 |
| 文章编号： | 1000-0887（2007）12-1483-10 |
| 收稿时间： | 2006-05-22 |
| 修稿时间： | 2006-05-22 |
Improved Proximal-Based Decomposition Method for Structured Monotone Variational Inequalities |
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| LI Min,YUAN Xiao-ming. Improved Proximal-Based Decomposition Method for Structured Monotone Variational Inequalities[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1483-1492 |
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| Authors: | LI Min YUAN Xiao-ming |
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| Affiliation: | Department of Management Science and Engineering, School of Economics and Management, Southeast University, Nanjing 210096, P. R. China; |
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| Abstract: | The proximal-based decomposition method was originally proposed by Chen and Teboulle(Math.Programming,1994,64(1):81-101) for solving convex minimization problems.This paper extended to solve monotone variational inequalities associated with separable structures with the improvements that the restrictive assumptions on the involved parameters are much relaxed,and thus makes it practical to solve the involved subproblems easily.Without additional assumptions,global convergence of the new method is proved under the same mild assumptions on the problem's data as the original method. |
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| Keywords: | decomposition inexact criterion proximal structured variational inequality |
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