The PRP conjugate gradient algorithm with a modified WWP line search and its application in the image restoration problems

Abstract

It is well known that the conjugate gradient algorithm is one of the most classic and useful methods for solving large-scale optimization problems, where the Polak-Ribière-Polyak(PRP) method is an important and effective conjugate gradient algorithm. However, the global convergence of the PRP conjugate gradient method can not be achieved when the WWP line search technique is used for a nonconvex function. In this paper, we propose a modified WWP line search technique for the PRP conjugate gradient algorithm. The new line search technique can guarantee the global convergence of the PRP method for general functions. The numerical results show that the PRP method with a new line search technique enables a practical computation and is effective in the image restoration problems.