A new class of efficient and globally convergent conjugate gradient methods in the Dai–Liao family

Abstract

In this paper, we propose a new conjugate gradient (CG) method which belongs to the CG methods of Dai–Liao family [New conjugacy conditions and related nonlinear conjugate gradient methods, Appl. Math. Optim. 43 (2001), pp. 87–101]. Babaie-Kafaki et al. [Two new conjugate gradient methods based on modified secant equations, J. Comput. Appl. Math. 234 (2010), pp. 1374–1386] made some modifications on the Yabe and Takano's CG approach [Global convergence properties of nonlinear conjugate gradient methods with modified secant condition, Comput. Optim. Appl. 28 (2004), pp. 203–225] and received some appealing results in theory and practice. Here, we introduce an efficient updating rule for the parameters of the Yabe and Takano's CG algorithm. Under some standard assumptions, we establish the global convergence property of the new suggested algorithm on uniformly convex and general functions. Numerical results on some testing problems from CUTEr collection show the priority of the proposed method to some existing CG methods in practice.