A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property

Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. However, the strong Wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods. This paper presents a new version of the conjugate gradient method, which converges globally provided the line search satisses the standard Wolfe conditions. The conditions on the objective function are also weak, which are similar to that required by the Zoutendijk condition.