Some global convergence properties of the Wei–Yao–Liu conjugate gradient method with inexact line search

In [Z.Wei, S. Yao, L. Liu, The convergence properties of some new conjugate gradient methods, Applied Mathematics and Computation 183 (2006) 1341–1350], Wei et al. proposed a new conjugate gradient method called WYL method which has good numerical experiments and some excellent properties such as βkWYL⩾0. In this paper, we prove that while tk⩽1-c2L‖gk‖2‖dk‖2, the sufficient descent condition can be satisfied at each iteration of the WYL method. Based on this, the global convergence of the WYL method with the standard Armijo line search and the generalized Wolfe–Powell line search is established.