Further studies on the Wei–Yao–Liu nonlinear conjugate gradient method

The Wei–Yao–Liu (WYL) method proposed by Wei et al. [Z. Wei, S. Yao, L. Liu, The convergence properties of some new conjugate gradient methods, Appl. Math. Comput. 183 (2006) 1341–1350] has been proved to converge globally for uniformly convex functions with exact line search and nonconvex functions with the strong Wolfe line search if the parameter σ∈(0,1/4)σ∈(0,1/4). In this paper, we further study the global convergence properties of the WYL method. We show that this method still converges globally for nonconvex optimization when the strong Wolfe line search with the parameter σ=1/4σ=1/4 or some Armijo type line searches are used.