American Institute of Mathematical Sciences

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October  2008, 4(4): 739-755. doi: 10.3934/jimo.2008.4.739

Guaranteed descent conjugate gradient methods with modified secant condition

Shishun Li 1, and  Zhengda Huang 1,

1. 

Department of Mathematics, Zhejiang University, Hangzhou 310027, China, China

Received  January 2007 Revised  July 2008 Published  October 2008

Conjugate gradient methods are typically used to solve large scale unconstrained optimization problems. Recently, Hager and Zhang (2006) proposed two guaranteed descent conjugate gradient methods. In this paper, following Hager and Zhang (2006), we will use the modified secant condition given by Zhang et al.(1999) to present two new descent conjugate gradient methods. An interesting feature of these new methods is that they take both the gradient and function value information. Under some suitable assumptions, global convergence properties for these methods are established. Numerical comparisons with the Hager-Zhang methods are given.
Keywords: conjugate gradient method, global convergence, line search, standard Wolfe conditions., Unconstrained optimization.
Mathematics Subject Classification: Primary: 65K05, 90C06, 90C30; Secondary: 49D2.
Citation: Shishun Li, Zhengda Huang. Guaranteed descent conjugate gradient methods with modified secant condition. Journal of Industrial and Management Optimization, 2008, 4 (4) : 739-755. doi: 10.3934/jimo.2008.4.739
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