Convergence properties of a class of nonlinear conjugate gradient methods

Conjugate gradient methods are a class of important methods for unconstrained optimization problems, especially when the dimension is large. In this paper, we study a class of modified conjugate gradient methods based on the famous LS conjugate gradient method, which produces a sufficient descent direction at each iteration and converges globally provided that the line search satisfies the strong Wolfe condition. At the same time, a new specific nonlinear conjugate gradient method is constructed. Our numerical results show that the new method is very efficient for the given test problems by comparing with the famous LS method, PRP method and CG-DESCENT method.