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E. G. Birgin and J. M. Martínez, “Structured Minimal- Memory Inexact Quasi-Newton Method and Secant Pre- conditioners for Augmented Lagrangian Optimization,” Computational Optimization and Applications, Vol. 39, No. 1, 2008, pp. 1-16. doi:10.1007/s10589-007-9050-z

has been cited by the following article:

• 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.