A modified conjugate gradient algorithm with backtracking line search technique for large-scale nonlinear equations

ABSTRACT

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.

Keywords:

• Conjugate gradient method
• acceleration scheme
• nonlinear equations
• descent property
• global convergence

2010 Mathematics Subject Classifications:

• 65K05
• 90C26

Additional information

Funding

This work was supported by the Natural Science Foundation of Guangxi Province [grant number 2015GXNSFGA139001] and National Natural Science Foundation of China [grant number 11261006, 11661009].