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Annals of Operations Research

, Volume 103, Issue 1–4, pp 161–173 | Cite as

Global Convergence of Conjugate Gradient Methods without Line Search

  • Jie Sun
  • Jiapu Zhang
Article

Abstract

Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: (1) The Fletcher–Reeves method, the Hestenes–Stiefel method, and the Dai–Yuan method applied to a strongly convex LC1 objective function; (2) The Polak–Ribière method and the Conjugate Descent method applied to a general, not necessarily convex, LC1 objective function.

conjugate gradient methods convergence of algorithms line search 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Jie Sun
    • 1
  • Jiapu Zhang
    • 2
  1. 1.Department of Decision SciencesNational University of SingaporeRepublic of Singapore
  2. 2.Department of MathematicsUniversity of MelbourneMelbourneAustralia

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