Global convergence of  modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property

Gaohang Yu; Lutai Guan; Guoyin Li

doi:10.3934/jimo.2008.4.565

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2008, Volume 4, Issue 3: 565-579. Doi: 10.3934/jimo.2008.4.565

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Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property

1.
Department of Scientific Computation and Computer Applications, Sun Yat-Sen University, Guangzhou, 510275
2.
Department of Mathematics, The Chinese University of Hong Kong Shatin, Hong Kong

Received: December 31, 2005

Revised: April 30, 2008

Published: June 2008

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Abstract

In this paper, we proposed two modified PRP conjugate gradient methods. It is a interesting feature that these new methods possess the sufficient descent property without assuming any line search condition and reduce to the standard PRP method when exact line search is used. Under some reasonable conditions, the global convergence is achieved for these methods. Preliminary numerical results show that these methods are efficient.

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Mathematics Subject Classification: Primary: 65K05, 90C30; Secondary: 49M37.

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Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property

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