A family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations

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Abstract

In this paper, we propose a family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations. They come from two modified conjugate gradient methods [W.Y. Cheng, A two term PRP based descent Method, Numer. Funct. Anal. Optim. 28 (2007) 1217–1230; L. Zhang, W.J. Zhou, D.H. Li, A descent modified Polak–Ribiére–Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal. 26 (2006) 629–640] recently proposed for unconstrained optimization problems. Under appropriate conditions, the global convergence of the proposed method is established. Preliminary numerical results show that the proposed method is promising.

MSC

90C25
90C33

Keywords

Conjugate gradient method
Nonmonotone line search
Global convergence

Cited by (0)

This work was supported by the 973 project grant 2004CB719402 and the NSF project of China grant 10771057.