Abstract
Based on an eigenvalue study, the sufficient descent condition of an extended class of the Hager-Zhang nonlinear conjugate gradient methods is established. As an interesting result, it is shown that the search directions of the CG_Descent algorithm satisfy the sufficient descent condition \(d_k^Tg_k<-\frac{7}{8}||g_k||^2\).
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Acknowledgments
This research was supported by Research Council of Semnan University. The author is grateful to an anonymous reviewer for his/her valuable suggestions helped to improve the presentation.
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Babaie-Kafaki, S. On the sufficient descent condition of the Hager-Zhang conjugate gradient methods. 4OR-Q J Oper Res 12, 285–292 (2014). https://doi.org/10.1007/s10288-014-0255-6
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DOI: https://doi.org/10.1007/s10288-014-0255-6