TITLE:
A Look at the Tool of BYRD and NOCEDAL
AUTHORS:
Linghua Huang, Guoyin Li, Gonglin Yuan
KEYWORDS:
Quasi-Newton Method, Unconstrained Minimization, Nonconvex Problem, Global Convergence
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.1 No.4,
December
9,
2011
ABSTRACT: 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.