| 求解线性规划问题的光滑型牛顿算法 |
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| 引用本文： | 孙秀萍,郑丕谔. 求解线性规划问题的光滑型牛顿算法[J]. 计算机工程与应用, 2008, 44(20): 30-35. DOI: 10.3778/j.issn.1002-8331.2008.20.010 |
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| 作者姓名： | 孙秀萍 郑丕谔 |
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| 作者单位： | 1.天津大学 理学院 数学系，天津 300072 2.天津大学 管理学院，天津 300072 |
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| 摘 要： | 对线性规划的最优性条件，给出一个扩展系统，设计一个连续化的光滑型算法求解该系统。所设计的算法的全局收敛性不需要添加任何假设条件。在每一个迭代点处，只需要解一个线性方程组和做一次线性搜索，比现有求解线性规划问题的连续化方法具有更好的收敛性质。
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| 关 键 词： | 线性规划 光滑型牛顿算法 全局收敛 严格互补解 |
| 收稿时间： | 2007-10-09 |
| 修稿时间： | 2008-1-15 |
Smoothing Newton algorithm for solving linear programs problem |
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| SUN Xiu-ping,ZHENG Pi-e. Smoothing Newton algorithm for solving linear programs problem[J]. Computer Engineering and Applications, 2008, 44(20): 30-35. DOI: 10.3778/j.issn.1002-8331.2008.20.010 |
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| Authors: | SUN Xiu-ping ZHENG Pi-e |
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| Affiliation: | 1.Department of Mathematics，School of Science，Tianjin University，Tianjin 300072，China 2.School of Management，Tianjin University，Tianjin 300072，China |
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| Abstract: | We propose a continuation method for solving the Linear Program(LP) by making use of an augmented system of its optimality conditions.The algorithm is shown to be globally convergent without requiring any assumption.It only needs to solve one system of linear equations and to perform one line search at each iteration.To the best of our knowledge this is the first continuation smoothing-type algorithm for solving the LP having the above desired convergence features. |
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| Keywords: | linear program smoothing Newton algorithm global convergence strictly complementary solution |
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