一种新的共轭梯度法
A New Conjugate Gradient Method
DOI: 10.12677/AAM.2016.54071, PDF, HTML, XML, 下载: 1,851  浏览: 2,255 
作者: 黎勇:百色学院数学与统计学院,广西 百色 ;袁功林:广西大学数学与信息科学学院,广西 南宁
关键词: 无约束优化共轭梯度法全局收敛性Unconstrained Optimization Conjugate Gradient Method Global Convergence
摘要: 本文设计了一个新的参数公式,在适当条件下,建立在此参数公式上的共轭梯度算法在WWP线搜索下全局收敛。初步的数值实验结果表明新算法是有效的。
Abstract: This paper has designed a new parameter formula. The conjugate gradient algorithm which based on the parameter formula is global convergence with WWP line search under appropriate condi-tions. Preliminary numerical results turn out that this new method is effective.
文章引用:黎勇, 袁功林. 一种新的共轭梯度法[J]. 应用数学进展, 2016, 5(4): 614-619. http://dx.doi.org/10.12677/AAM.2016.54071

参考文献

[1] 戴彧虹, 袁亚湘. 非线性共轭梯度法[M]. 上海: 上海科技出版社, 1999.
[2] Powell, M.J.D. (1984) Nonconvex Minimization Calculations and the Conjugate Gradient Method. Springer-Verlag, Berlin, 122-141.
http://dx.doi.org/10.1007/bfb0099521
[3] Wei, Z., Yao, S. and Liu, L. (2006) The Convergence Properties of Some New Conjugate Gradient Methods. Applied Mathematics and Computation, 183, 1341-1350.
http://dx.doi.org/10.1016/j.amc.2006.05.150
[4] Huang, H., Wei, Z. and Yao, S. (2007) The Proof of the Sufficient Descent Condition of the Wei-Yao-Liu Conjugate Gradient Method under the Strong Wolfe-Powell Line Search. Applied Mathematics and Computation, 189, 1241- 1245.
http://dx.doi.org/10.1016/j.amc.2006.12.006
[5] Lu, S., Wei, Z. and Mo, L. (2011) Some Global Convergence Properties of the Wei-Yao-Liu Conjugate Gradient Method with Inexact Line Search. Applied Mathematics and Computation, 217, 7132-7137.
http://dx.doi.org/10.1016/j.amc.2011.01.097
[6] Huang, H. and Lin, S. (2014) A Modified Wei-Yao-Liu Conjugate Gradient Method for Unconstrained Optimization. Applied Mathematics and Computation, 231, 179-186.
http://dx.doi.org/10.1016/j.amc.2014.01.012
[7] 黎勇. 一类新的修正PRP共轭梯度法[J]. 武汉理工大学学报(交通科学与工程版), 2012, 36(2): 437-440.
[8] Hager, W.W. and Zhang, H. (2006) A Survey of Nonlinear Conjugate Gradient Methods. Pacific journal of Optimization, 2, 35-58.