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Journal of Optimization Theory and Applications

, Volume 78, Issue 3, pp 599–604 | Cite as

Rate of convergence of a generalization of Newton's method

  • Y. Benadada
  • J. P. Crouzeix
  • J. A. Ferland
Technical Note

Abstract

The Newton's method for finding the root of the equation Θ(t)=0 can be easily generalized to the case where Θ is monotone, convex, but not differentiable. Then, the convergence is superlinear. The purpose of this note is to show that the convergence is only superlinear. Indeed, for all α∈(1, 2), we exhibit an example where the convergence of the iterates is exactly α.

Key Words

Newton's method rate of convergence 

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References

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    Benadada, Y.,Approches de Résolution du Problème de Programmation Fractionnaire Généralisé, PhD Thesis, Université de Montréal, Montréal, Québec, Canada, 1989.Google Scholar
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    Schaible, S.,Fractional Programming 2: On Dinkelbach's Algorithm, Management Science, Vol. 22, pp. 868–873, 1976.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Y. Benadada
    • 1
  • J. P. Crouzeix
    • 2
  • J. A. Ferland
    • 3
  1. 1.Départment de MathématiquesFaculté des SciencesTetouanMaroc
  2. 2.Centre National de la Recherche ScientifiqueMathématiques Appliquées, SciencesAubièreFrance
  3. 3.Department d'Informatique et de Recherche OpérationnelleUniversité de MontréalMontréalCanada

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