A descent PRP conjugate gradient method for unconstrained optimization

Abstract

It is well known that the sufficient descent condition is very important to the global convergence of the nonlinear conjugate gradient methods. Also, the direction generated by a conjugate gradient method may not be a descent direction. In this paper, we propose a new Armijo-type line search algorithm such that the direction generated by the PRP conjugate gradient method has the sufficient descent property and ensures the global convergence of the PRP conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions. We also present some numerical results to show the efficiency of the proposed method.The results show the efficiency of the proposed method in the sense of the performance profile introduced by Dolan and More.