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Global convergence of some modified PRP nonlinear conjugate gradient methods

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Abstract

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.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Zhi-feng Dai

  2. College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha, 410114, China

    Zhi-feng Dai & Bo-Shi Tian

Authors
  1. Zhi-feng Dai
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  2. Bo-Shi Tian
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Correspondence to Zhi-feng Dai.

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Dai, Zf., Tian, BS. Global convergence of some modified PRP nonlinear conjugate gradient methods. Optim Lett 5, 615–630 (2011). https://doi.org/10.1007/s11590-010-0224-8

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  • DOI: https://doi.org/10.1007/s11590-010-0224-8

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