A modified CG-DESCENT method for unconstrained optimization

Recently, Hager and Zhang (2005) [11] proposed a new conjugate gradient method which generates sufficient descent direction gkTdk≤−7/8‖gk‖2, this property is independent of the line search used. In this paper, we take a modification of this method, such that the sufficient descent direction satisfies gkTdk=−‖gk‖2, this property is also independent of the line search used. Under appropriate conditions, we prove that the proposed method is globally convergent. Moreover, we give a sufficient condition for the global convergence of the proposed general method. The numerical results show that the proposed method is efficient.