A Modified Conjugate Gradient Method for Unconstrained Optimization

Conjugate gradient methods are an important class of methods for solving unconstrained optimization problems, especially for large-scale problems. Recently, they have been studied in depth. In this paper, we further study the conjugate gradient method for unconstrained optimization. We focus our attention to the descent conjugate gradient method. This paper presents a modified conjugate gradient method. An interesting feature of the presented method is that the direction is always a descent direction for the objective function. Moreover, the property is independent of the line search used. Under mild conditions, we prove that the modified conjugate gradient method with Armijo-type line search is globally convergent. We also present some numerical results to show the efficiency of the proposed method.