On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

Abstract EN

Recently, Zhang et al.

proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense that lim infk→∞∥∇f(xk)∥=0 when an Armijo-type line search is used.

In this paper, motivated by the line searches proposed by Shi et al.

and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense that limk→∞∥∇f(xk)∥=0 under the two new line searches.

Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.