| 垂直线性互补问题的一步全局线性和局部二次收敛光滑Newton法 |
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| 引用本文： | 张立平,高自友.垂直线性互补问题的一步全局线性和局部二次收敛光滑Newton法[J].应用数学和力学,2003,24(6):653-660. |
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| 作者姓名： | 张立平 高自友 |
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| 作者单位： | 1.清华大学, 数学科学系, 北京, 100084; |
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| 基金项目： | 国家自然科学基金资助项目(10201001)，国家杰出青年基金资助项目(70225005) |
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| 摘 要： | 基于凝聚函数,提出一个求解垂直线性互补问题的光滑Newton法.该算法具有以下优点:(i)每次迭代仅需解一个线性系统和实施一次线性搜索;(ⅱ)算法对垂直分块P0矩阵的线性互补问题有定义且迭代序列的每个聚点都是它的解.而且,对垂直分块P0+R0矩阵的线性互补问题,算法产生的迭代序列有界且其任一聚点都是它的解;(ⅲ)在无严格互补条件下证得算法即具有全局线性收敛性又具有局部二次收敛性.许多已存在的求解此问题的光滑Newton法都不具有性质(ⅲ).
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| 关 键 词： | 垂直线性互补 光滑Newton法 全局线性收敛 局部二次收敛 |
| 文章编号： | 1000-0887(2003)06-0653-08 |
| 收稿时间： | 2002-01-29 |
| 修稿时间： | 2002年1月29日 |
Global Linear and Quadratic One-Step Smoothing Newton Method for Vertical Linear Complementarity Problems |
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| Institution: | 1.Department of Methematical Sciences, Tsinghua University, Beijing 100084, P. R. China;2.School of Traffic and Transportation, Northern Jiaotong University, Beijing 100044, P. R. China |
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| Abstract: | A one-step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so-called aggregation function. The proposed algorithm has the following good features: (i) it solves only one linear system of equations and does only one line search at each iteration; (ⅱ) it is well-defined for the vertical linear complementarity problem with vertical block P0 matrix and any accumulation point of iteration sequence is its solution. Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P0+R0 matrix; (ⅲ) it has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property(ⅲ). |
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| Keywords: | vertical linear complementarity problems smoothing Newton method global linear convergence quadratic convergence |
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