| 基于光滑逼近函数的高阶牛顿法求解凸二次规划 |
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| 引用本文： | 雍龙泉,贾伟,黎延海. 基于光滑逼近函数的高阶牛顿法求解凸二次规划[J]. 科学技术与工程, 2021, 21(6): 2151-2156. DOI: 10.3969/j.issn.1671-1815.2021.06.004 |
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| 作者姓名： | 雍龙泉 贾伟 黎延海 |
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| 作者单位： | 陕西理工大学数学与计算机科学学院,汉中723001;陕西理工大学,陕西省工业自动化重点实验室,汉中723001;陕西理工大学数学与计算机科学学院,汉中723001 |
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| 基金项目： | 国家自然科学基金(11401357) |
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| 摘 要： | 研究绝对值函数的3个光滑逼近函数的性质,并采用图像展示了逼近效果.进而提出求解凸二次规划问题的新方法:将凸二次规划转化为非线性方程组,采用光滑逼近函数进行处理,得到光滑非线性方程组,进而利用高阶牛顿法进行求解.数值实验结果表明:本文方法收敛快、迭代次数少.
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| 关 键 词： | 凸二次规划 光滑逼近函数 高阶牛顿法 绝对值函数 非线性方程组 |
| 收稿时间： | 2020-06-15 |
| 修稿时间： | 2020-12-02 |
HighSOrderSNewtonsSMethod for Convex Quadratic ProgrammingBased on Smooth Approximation Function |
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| Yong Longquan,Jia Wei,Li Yanhai. HighSOrderSNewtonsSMethod for Convex Quadratic ProgrammingBased on Smooth Approximation Function[J]. Science Technology and Engineering, 2021, 21(6): 2151-2156. DOI: 10.3969/j.issn.1671-1815.2021.06.004 |
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| Authors: | Yong Longquan Jia Wei Li Yanhai |
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| Affiliation: | School of Mathematics and Computer Science,Shaanxi University of Technology,School of Mathematics and Computer Science,Shaanxi University of Technology,School of Mathematics and Computer Science,Shaanxi University of Technology |
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| Abstract: | Properties of three smooth approximating functions for absolute value function are studied, and approximation degree is shown by images. Then a method for convex quadratic programming is proposed. After transforming convex quadratic programming into nonsmooth nonlinear equation system, and smoothing by smoothing approximation function, thus weSobtain smooth nonlinear equations, which can be solved by highSorderSNewtonsSmethod. Numerical results show that the method has fast convergence and fewer iterations. |
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| Keywords: | convex quadratic programming smooth approximating function highSorderSNewtonsSmethod absolute value function nonlinear equation system |
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