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Journal of Optimization Theory and Applications

, Volume 71, Issue 2, pp 399–405 | Cite as

Global convergence result for conjugate gradient methods

  • Y. F. Hu
  • C. Storey
Technical Note

Abstract

Conjugate gradient optimization algorithms depend on the search directions,
$$\begin{gathered} s^{(1)} = - g^{(1)} , \hfill \\ s^{(k + 1)} = - g^{(k + 1)} + \beta ^{(k)} s^{(k)} ,k \geqslant 1, \hfill \\ \end{gathered} $$
with different methods arising from different choices for the scalar β(k). In this note, conditions are given on β(k) to ensure global convergence of the resulting algorithms.

Key Words

Conjugate gradient algorithms global convergence 

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References

  1. 1.
    Al-Baali, M.,Descent Property and Global Convergence of the Fletcher-Reeves Method with Inexact Line Searches, IMA Journal of Numerical Analysis, Vol. 5, No. 1, pp. 121–124, 1985.Google Scholar
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    Touati-Ahmed, D., andStorey, C.,Globally Convergent Hybrid Conjugate Gradient Methods, Journal of Optimization Theory and Applications, Vol. 64, No. 2, pp. 379–397, 1990.Google Scholar
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    Gilbert, J. C., andNocedal, J.,Global Convergence Properties of Conjugate Gradient Methods for Optimization, Rapport de Recherche No. 1268, Institut National de Recherche en Informatique et Automatique, Domaine de Voluceau, Rocquencourt, Le Chesnay, France, 1990.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Y. F. Hu
    • 1
  • C. Storey
    • 1
  1. 1.Department of Mathematical SciencesLoughborough University of TechnologyLoughboroughEngland

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