| 基于尺度中心路径的预估—矫正光滑化算法 |
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| 引用本文： | 刘长河,甘从辉,丁艳风.基于尺度中心路径的预估—矫正光滑化算法[J].西安文理学院学报,2010,13(2):31-35. |
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| 作者姓名： | 刘长河 甘从辉 丁艳风 |
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| 作者单位： | [1]河南科技大学理学院,河南洛阳471003 [2]西安电子科技大学理学院,陕西西安710071 [3]河南科技大学电子信息工程学院,河南洛阳471003 [4]郑州大学升达经贸管理学院,河南郑州451191 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 对于求解线性规划问题提出了一个基于尺度中心路径的预估-矫正光滑化方法.在适当的假设条件下,证明了方法的全局和局部二次收敛性.特别,在方法的局部二次收敛性分析中,不需要假定线性规划的解是唯一的.文中的方法可以推广到P0-线性互补问题和单调线性互补问题.
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| 关 键 词： | 线性规划 尺度中心路径 光滑化方法 二次收敛 |
Predictor-Corrector Smoothing Methods Based on a Scaled Central Path for Linear Programming |
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| LIU Chang-he,GAN Cong-hui,DING Yan-feng.Predictor-Corrector Smoothing Methods Based on a Scaled Central Path for Linear Programming[J].Journal of Xi‘an University of Arts & Science:Natural Science Edition,2010,13(2):31-35. |
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| Authors: | LIU Chang-he GAN Cong-hui DING Yan-feng |
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| Institution: | 1. College of Science, Henan University of Science ＆ Technology, Luoyang 471003, China; 2. College of Science, Xidian University, Xi＇ an 710071, China; 3. College of Electronic Information Engineering, Henan University of Science ＆ Technology, Luoyang 471003, China; 4. Department of Common Disciplines, Shengda College of Economics, Trade ＆ Management, Zhengzhou University, Zhengzhou 451191, China) |
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| Abstract: | This paper presents a predictor-corrector smoothing-type method based on a scaled central path for the solution of linear programs. Its main idea is to reformulate the primal-dual optimality conditions as a nonlinear and non-smooth system of equations, and to apply a Newton-type method to a smooth approximation of this non-smooth system. The method presented here is shown to be globally and locally quadratically convergent under reasonable assumptions （ which do not imply that the solution set consists of a single element）. The proposed method in this paper can also be extended to solve and monotone linear complementarity problems. |
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| Keywords: | linear programming scaled central path smoothing method quadratic convergence |
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