Optimization Letters

, Volume 5, Issue 4, pp 615–630 | Cite as

Global convergence of some modified PRP nonlinear conjugate gradient methods

  • Zhi-feng DaiEmail author
  • Bo-Shi Tian
Original Paper


Recently, similar to Hager and Zhang (SIAM J Optim 16:170–192, 2005), Yu (Nonlinear self-scaling conjugate gradient methods for large-scale optimization problems. Thesis of Doctors Degree, Sun Yat-Sen University, 2007) and Yuan (Optim Lett 3:11–21, 2009) proposed modified PRP conjugate gradient methods which generate sufficient descent directions without any line searches. In order to obtain the global convergence of their algorithms, they need the assumption that the stepsize is bounded away from zero. In this paper, we take a little modification to these methods such that the modified methods retain sufficient descent property. Without requirement of the positive lower bound of the stepsize, we prove that the proposed methods are globally convergent. Some numerical results are also reported.


Unconstrained optimization Conjugate gradient method Line search Sufficient descent property Global convergence 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.College of Mathematics and EconometricsHunan UniversityChangshaChina
  2. 2.College of Mathematics and Computational ScienceChangsha University of Science and TechnologyChangshaChina

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