# American Institute of Mathematical Sciences

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

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

 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.
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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