摘要
谱共轭梯度法含有两个方向调控参数,是一种结合共轭梯度法和谱梯度法的无约束优化方法。本文建立新的共轭参数和谱参数,提出无约束优化问题的两个谱共轭梯度法,这两个新方法在精确线搜索下等价于FR共轭梯度法。然后,证明了算法1在Wolfe线搜索下和算法2在Armijo线搜索下的全局收敛性,并给出了算法的数值实验结果,验证了算法的有效性。
Spectral conjugate gradient method contains two directions regulatory parameters is a kind of method for unconstrained op- timization that combines conjugate gradient method with spectral gradient method. In this paper, based on the new conjugate param- eters and spectral parameters, two spectral conjugate gradient methods are proposed; the corresponding methods are equivalent to the FR conjugate gradient method when the line search is exact. Moreover, the global convergence of algorithm 1 with Wolfe line search is proved, the global convergence of algorithm 2 with standard Armijo line search is proved. The given numerical results show that the new methods are efficient.
出处
《重庆师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2015年第2期1-6,共6页
Journal of Chongqing Normal University:Natural Science
基金
广西高校科研项目(No.ZD2014143)
广西重点培育学科(应用数学)建设项目(No.桂教科研[2013]16)
广西民族师范学院科研项目(No.2013RCGG002)
关键词
无约束优化
谱共轭梯度法
全局收敛性
unconstrained optimization
spectral conjugate gradient method
global convergence
