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Global convergence result for conjugate gradient methods

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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.

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References

  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 

  2. Powell, M. J. D.,Nonconvex Minimization Calculations and the Conjugate Gradient Method, Report No. DAMTP 1983/NA14, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England, 1983.

    Google Scholar 

  3. 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 

  4. 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 

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Communicated by L. C. W. Dixon

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Hu, Y.F., Storey, C. Global convergence result for conjugate gradient methods. J Optim Theory Appl 71, 399–405 (1991). https://doi.org/10.1007/BF00939927

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  • DOI: https://doi.org/10.1007/BF00939927

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