Using a new hybrid conjugate gradient method with descent property

Abstract

The conjugate gradient method was an efficient technique for solving optimization problems. In this paper, we propose a new efficient (CG) coefficient bk,  is computed as a convex combination of Salleh and Alhawarat algorithm and CG-Descent algorithm. We prove the sufficient descent condition and the global convergence of the proposed method. It is established that the ak  satisfies the strong Wolfe line search conditions. The numerical results indicate that our method is robust and competitive.