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

C.Y. Wang; M.X. Li

doi:10.3934/jimo.2005.1.193

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2005, Volume 1, Issue 2: 193-200. Doi: 10.3934/jimo.2005.1.193

This issue Previous Article Analysis of monotone gradient methods Next Article An iterative method for general variational inequalities

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

C.Y. Wang^1, and
M.X. Li¹

1.
Dept. of Appl. Math., Dalian University of Technology, Dalian, Liaoning, 116024

Received: April 30, 2004

Revised: September 30, 2004

Published: March 2005

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Abstract

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.

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Mathematics Subject Classification: 90C30, 49D27.

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