American Institute of Mathematical Sciences

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April  2005, 1(2): 193-200. doi: 10.3934/jimo.2005.1.193

Convergence property of the Fletcher-Reeves conjugate gradient method with errors

C.Y. Wang 1, and  M.X. Li 1,

1. 

Dept. of Appl. Math., Dalian University of Technology, Dalian, Liaoning, 116024, China, China

Received  May 2004 Revised  October 2004 Published  April 2005

In this paper, we consider a new kind of Fletcher-Reeves (abbr. FR) conjugate gradient method with errors, which is broadly applied in neural network training. Its iterate formula is $x_{k+1}=x_{k}+\alpha_{k}(s_{k}+\omega_{k})$, where the main direction $s_{k}$ is obtained by FR conjugate gradient method and $\omega_{k}$ is accumulative error. The global convergence property of the method is proved under the mild assumption conditions.
Keywords: global convergence, error., Conjugate gradient method.
Mathematics Subject Classification: 90C30, 49D2.
Citation: C.Y. Wang, M.X. Li. Convergence property of the Fletcher-Reeves conjugate gradient method with errors. Journal of Industrial & Management Optimization, 2005, 1 (2) : 193-200. doi: 10.3934/jimo.2005.1.193
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