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A Look at the Tool of BYRD and NOCEDAL

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DOI: 10.4236/ajcm.2011.14028    3,757 Downloads   7,011 Views  


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.

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L. Huang, G. Li and G. Yuan, "A Look at the Tool of BYRD and NOCEDAL," American Journal of Computational Mathematics, Vol. 1 No. 4, 2011, pp. 240-246. doi: 10.4236/ajcm.2011.14028.


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