Author(s)

Linghua Huang, Guoyin Li, Gonglin Yuan

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A power tool for the analysis of quasi-Newton methods has been proposed by Byrd and Nocedal ([1], 1989). The purpose of this paper is to make a study to the basic property (BP) given in [1]. As a result of the BP, a sufficient condition of global convergence for a class of quasi-Newton methods for solving unconstrained minimization problems without convexity assumption is given. A modified BFGS formula is designed to match the requirements of the sufficient condition. The numerical results show that the proposed method is very encouraging.

Quasi-Newton Method, Unconstrained Minimization, Nonconvex Problem, Global Convergence

Huang, L. , Li, G. and Yuan, G. (2011) A Look at the Tool of BYRD and NOCEDAL. American Journal of Computational Mathematics, 1, 240-246. doi: 10.4236/ajcm.2011.14028.