Journal of Optimization Theory and Applications

, Volume 71, Issue 2, pp 399–405

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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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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