A new spectral Polak-Ribière-Polyak conjugate gradient method

Abstract

By combining the spectral gradient and Polak-Ribière-Polyak (PRP) methods, a new spectral PRP conjugate gradient method is proposed to solve large-scaled unconstrained optimization problems.The method satisfies the famous conjugacy condition: d T k y k-1 = 0, independent of any line search.The direction at each iteration generated by the proposed method is downward for the general objective function without any line search.Under the standard Wolfe line search, we prove that the proposed method is globally convergent.Finally, the proposed method is compared with the PRP method and the scaled PRP method using a classical set of problems.