American Institute of Mathematical Sciences

Advanced
July  2008, 4(3): 565-579. doi: 10.3934/jimo.2008.4.565

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

Gaohang Yu 1, , Lutai Guan 1, and  Guoyin Li 2,

1. 

Department of Scientific Computation and Computer Applications, Sun Yat-Sen University, Guangzhou, 510275, China, China
2. 

Department of Mathematics, The Chinese University of Hong Kong Shatin, Hong Kong, China

Received  January 2006 Revised  May 2008 Published  July 2008

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.
Keywords: global convergence., conjugate gradient method, Unconstrained optimization, nonconvex minimization.
Mathematics Subject Classification: Primary: 65K05, 90C30; Secondary: 49M3.
Citation: Gaohang Yu, Lutai Guan, Guoyin Li. Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property. Journal of Industrial and Management Optimization, 2008, 4 (3) : 565-579. doi: 10.3934/jimo.2008.4.565
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