A new conjugate gradient method and its global convergence under the exact line search

Abstract

The conjugate gradient methods are numerously used for solving nonlinear unconstrained optimization problems, especially of large scale. Their wide applications are due to their simplicity and low memory requirement. To analyze conjugate gradient methods, two types of line searches are used; exact and inexact. In this paper, we present a new method of nonlinear conjugate gradient methods under the exact line search. The theoretical analysis shows that the new method generates a descent direction in each iteration and globally convergent under the exact line search. Moreover, numerical experiments based on comparing the new method with other well known conjugate gradient methods show that the new is efficient for some unconstrained optimization problems.