Numerical Algorithms

, Volume 50, Issue 1, pp 1–16

Two modified Dai-Yuan nonlinear conjugate gradient methods

Original Paper


In this paper, we propose two modified versions of the Dai-Yuan (DY) nonlinear conjugate gradient method. One is based on the MBFGS method (Li and Fukushima, J Comput Appl Math 129:15–35, 2001) and inherits all nice properties of the DY method. Moreover, this method converges globally for nonconvex functions even if the standard Armijo line search is used. The other is based on the ideas of Wei et al. (Appl Math Comput 183:1341–1350, 2006), Zhang et al. (Numer Math 104:561–572, 2006) and possesses good performance of the Hestenes-Stiefel method. Numerical results are also reported.


Conjugate gradient method Global convergence 

Mathematics Subject Classifications (2000)

90C30 65K05 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.College of Mathematics and Computational ScienceChangsha University of Science and TechnologyChangshaChina

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