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修正PRP共轭梯度法的全局收敛性及其数值结果

莫降涛,顾能柱,韦增欣   

  1. 广西大学数学与信息科学学院;广西大学数学与信息科学学院;广西大学数学与信息科学学院 广西南宁530004 西安交通大学理学院;西安710049;广西南宁530004;广西南宁530004
  • 出版日期:2007-01-20 发布日期:2007-01-20

莫降涛,顾能柱,韦增欣. 修正PRP共轭梯度法的全局收敛性及其数值结果[J]. 数值计算与计算机应用, 2007, 28(1): 56-62.

GLOBAL CONVERGENCE OF A MODIFIED PRP CONJUGATE GRADIENT METHOD AND ITS NUMERICAL RESULTS

  1. Ms Jiangtao (College of Mathematics and Information Science,Guangxi University,Nanning 530004,Guangxi,China;College of Science,Xian Jiaotong University,Xi'an 710049,China) Gu Nengzhu Wei Zengxin (College of Mathematics and Information Science,Guangxi University,Nanning 530004,Guangxi,China)
  • Online:2007-01-20 Published:2007-01-20
本文提出了一种求解无约束优化问题的修正PRP共轭梯度法.算法采用一个新的公式计算参数,避免了产生较小的步长.在适当的条件下,证明了算法具有下降性质,并且在采用强Wolfe线搜索时,算法是全局收敛的.最后,给出了初步的数值试验结果.
In this paper,we propose a modified Polak-Ribière-Polyak conjugate gradient method for unconstrained optimization.We develop a new formula for parameter which can prevent the algorithm generate small stepsizes.Under mild conditions, we prove that the method possesses descent property and is global convergence with the strong Wolfe line search.Encouraging numerical experiments are presented.
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