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

Authors:
Wanyou Cheng;Yunhai Xiao;Qing-Jie Hu
Affiliations:
College of Software, Dongguan University of Technology, Dongguan 523000, PR china;Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, 475004, PR China;Department of Information, Hunan Business College, Changsha, 410205, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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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-Ribiere-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.