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 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 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.
"On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/283215