A DESCENT PRP CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION

Abstract

It is well known that the sucient 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 sucient descent property and ensures the global convergence of the PRP conjugate gradient method for the unconstrained minimization of nonconvex dierentiable functions. We also present some numerical results to show the eciency of the proposed method.The results show the eciency of the proposed method in the sense of the performance prole introduced by Dolan and More.

Keywords

• Unconstrained optimization,Armijo-type line search,Conjugate gradient method,sucient descent,Global convergence.

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