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

Lijun Li, Weijun Zhou


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.

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conjugate gradients; PRP method; strong convergence; linear convergence

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DOI: http://dx.doi.org/10.21914/anziamj.v55i0.7098

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