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D. Li and M. Fukushima, “A Modified BFGS Method and Its Global Convergence in Nonconvex Minimiza- tion,” Journal of Computational and Applied Mathemat- ics, Vol. 129, No. 1-2, 2001, pp. 15-35. doi:10.1016/S0377-0427(00)00540-9

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.