On the convergence properties of the modified Polak--Ribiere--Polyak method with the standard Armijo line search

Authors

  • Lijun Li Department of Mathematics, Changsha University of Science and Technology, Changsha 410004
  • Weijun Zhou Department of Mathematics, Changsha University of Science and Technology, Changsha 410004

DOI:

https://doi.org/10.21914/anziamj.v55i0.7098

Keywords:

conjugate gradients, PRP method, strong convergence, linear convergence

Abstract

Zhang et al. [IMA J. Numer. Anal., 26 (2006) 629--640] proposed a modified Polak--Ribiere--Polyak method for non-convex optimization and proved its global convergence with some backtracking type line search. We further study its convergence properties. Under the standard Armijo line search condition, we show that the modified Polak--Ribiere--Polyak method has better global convergence property and locally \(R\)-linear convergence rate for non-convex minimization. Some preliminary numerical results are also reported to show its efficiency. References
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Published

2014-04-16

Issue

Section

Articles for Electronic Supplement