The global convergence properties of a conjugate gradient method

Conjugate gradient methods are the most famous methods for solving nonlinear unconstrained optimization problems, especially large scale problems. That is, for its simplicity and low memory requirement. The strong Wolfe line search are usually used in practice for the analyses and implementations of conjugate gradient methods. In this paper, we present a new method of nonlinear conjugate gradient method with strong Wolfe line search for unconstrained optimization problems. Under some assumptions, the sufficient descent property and the global convergence are given. The numerical results show that our new method is efficient for some unconstrained optimization problems.