摘要
应用Powell对称化技术于Polak-Ribiere-Polyak共轭梯度法,提出了一种下降对称的Polak-Ribiere-Polyak共轭梯度法.对任意线性搜索,它都满足下降性质.在强Wolfe线搜索的条件下,利用矩阵的谱分析和Zoutendijk条件,证明了此算法的全局收敛性.最后,通过数值实验并且与Polak-Ribiere+(PR+)算法作比较,验证了该算法的性能和有效性与实用性.
Applying Powell symmetrical technique to the Polak-Ribiere-Polyak conjugate gradient method, a descent symmetrical Polak-Ribiere-Polyak conjugate gradient method was proposed, which satisfied the descent property for any line search. Under the strong Wolfe line search conditions, the global convergence of the new method was testified by the spectral analysis of matrix and Zoutendijk condition. Finally, compared with the Polak-Ribiere^＋ （PR^＋） algorithm, the performance and the availability of the new algorithm are verified by numerical experiments.
出处
《天津大学学报》
EI
CAS
CSCD
北大核心
2010年第4期367-372,共6页
Journal of Tianjin University(Science and Technology)
基金
国家自然科学基金资助项目(60874034)
国家自然科学基金青年科学基金资助项目(60704015)
关键词
共轭梯度法
全局最优化
算法
对称化技术
下降性质
线搜索
谱分析
全局收敛性
conjugate gradient method
global optimization
algorithm
symmetrical technique
descent property
line search
spectral analysis
global convergence
