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In this paper, the Hager–Zhang (HZ) conjugate gradient (CG) algorithm is studied for large-scale smooth optimization problems. (i) Some results of the HZ CG method for smooth unconstrained optimization problems are given, and a modified HZ (MHZ) CG method is proposed; (ii) the HZ and MHZ CG methods for nonlinear equations are analysed, the global convergence is established and numerical results for large-scale nonlinear equation problems are reported (1,00,000 variables). [ABSTRACT FROM AUTHOR]

Conjugate gradient methods are widely used for solving unconstrained optimization and nonlinear equations, specially in large-scale cases. Since they own the attractive practical factors of simple computation and low memory requirement, interesting theoretical features of curvature information and strong global convergence. In this paper, we present a modified conjugate gradient algorithm by line search method with acceleration scheme for nonlinear symmetric equations. Furthermore, the proposed method not only possess descent property but also owns global convergence in mild conditions. Numerical results also indicate that the presented method is much more effective than the other methods for the test problems. [ABSTRACT FROM PUBLISHER]