| 基于尺度中心路径的求解SCLP的非单调光滑牛顿算法 |
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| 引用本文： | 倪铁,刘晓红.基于尺度中心路径的求解SCLP的非单调光滑牛顿算法[J].数学物理学报(A辑),2014,34(2):378-392. |
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| 作者姓名： | 倪铁 刘晓红 |
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| 作者单位： | 1.辽宁工程技术大学 工商管理学院 辽宁 葫芦岛 125105;
2.天津大学理学院数学系 天津 300072 |
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| 基金项目： | 国家自然科学基金(10471126, 10371109)、浙江省自然科学基金(101016)和浙江省哲学社会科学规划常规性课题(06CGYJ21YBQ)资助. |
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| 摘 要： | 基于CHKS光滑函数的修改性版本,该文提出了一个带有尺度中心路径的求解对称锥线性规划(SCLP)的非单调光滑牛顿算法.通过应用欧氏若当代数理论,在适当的假设下,证明了该算法是全局收敛和超线性收敛的.数值结果表明了算法的有效性.
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| 关 键 词： | 线性规划 对称锥 欧氏若当代数 光滑算法 尺度中心路径 非单调线搜索 |
| 收稿时间： | 2012-03-06 |
| 修稿时间： | 2013-09-18 |
Non-Monotone Smoothing Newton Algorithm for SCLP Based on a Scaled Central Path |
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| NI Tie,LIU Xiao-Hong.Non-Monotone Smoothing Newton Algorithm for SCLP Based on a Scaled Central Path[J].Acta Mathematica Scientia,2014,34(2):378-392. |
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| Authors: | NI Tie LIU Xiao-Hong |
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| Institution: | 1.College of Business Administration, Liaoning Technical University, Liaoning Huludao 125105;
2.Department of Mathematics, School of Science, Tianjin University, Tianjin 300072 |
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| Abstract: | Based on a modified version of the Chen-Harker-Kanzow-Smale (CHKS) smoothing function, this paper investigates a non-monotone smoothing Newton algorithm with a scaled central path for solving linear programming over symmetric cones (SCLP). By using the theory of Euclidean Jordan algebras, we show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. Some preliminary numerical results is shown that our algorithm proposed is promising. |
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| Keywords: | Linear programmingzz Symmetric conezz Euclidean Jordan algebrazz Smoothing algorithmzz Scaled central pathzz Non-monotone line searchzz |
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