The convergence rate of a restart MFR conjugate gradient method with inexact line search

In this paper, we investigate the convergence rate of the modified Fletcher–Reeves (MFR) method proposed by Zhang et al. [L. Zhang, W.J. Zhou, D.H. Li, Global convergence of a modified Fletcher–Revves conjugate gradient method with Armijo-type line search, Numer. Math. 104 (2006) 561–572.]. Under reasonable conditions, we show that the MFR method with some inexact line search will be nn-step superlinearly and even quadratically convergent if some restart technique is used. Some numerical results are also reported to verify the theoretical results.