Guaranteed descent conjugate gradient methods with modified secant condition

Shishun Li; Zhengda Huang

doi:10.3934/jimo.2008.4.739

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2008, Volume 4, Issue 4: 739-755. Doi: 10.3934/jimo.2008.4.739

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Guaranteed descent conjugate gradient methods with modified secant condition

Shishun Li^1, and
Zhengda Huang^1,

1.
Department of Mathematics, Zhejiang University, Hangzhou 310027

Received: December 31, 2006

Revised: June 30, 2008

Published: September 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 65K05, 90C06, 90C30; Secondary: 49D27.

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