理论数学

Vol.1 No.1 (April 2011)

修改的DY和HS共轭梯度算法及其全局收敛性
Modified DY and HS Conjugate Gradient Algorithms and Ther Global Convergence

 

作者:

李向荣

 

关键词:

共轭梯度方法分下降性全局收敛性Conjugate Gradient Method Sufficient Descent Property Global Convergence

 

摘要:

Yuan[16]提出了修改的PRP共轭梯度方法,该方法能保证参数 非负且搜索方向在不需要任何线搜索下具有充分下降性。作者也将此技术推广到其它共轭梯度方法中,并给出了修改的公式,但是没有给出具体的收敛性证明。本文的主要工作就是分析修改的DY和HS共轭梯度方法的性质:充分下降性和全局收敛性,同时给出数值检验结果。

Yuan[16] proposed a modified PRP conjugate gradient method which can ensure that the scalar holds and the search direction possesses the sufficient descent property without any line search. This technique has been extended to other conjugate gradient methods, but the convergence has been not given. In this paper, our purpose is to analyze the property of DY and HS: sufficient descent property and global convergence, moreover numerical results are shown.

文章引用:

李向荣 (2011) 修改的DY和HS共轭梯度算法及其全局收敛性。 理论数学, 1, 1-7. doi: 10.12677/pm.2011.11001

 

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