A descent extension of the Polak–Ribière–Polyak conjugate gradient method

Based on an eigenvalue analysis, a descent class of two-parameter extension of the conjugate gradient method proposed by Polak and Ribière (1969), and Polyak (1969) is suggested. It is interesting that the one-parameter class of descent conjugate gradient methods proposed by Yu et al. (2008) is a member of the suggested class. Global convergence analysis for the methods of the suggested class is made briefly. Preliminary numerical results are reported; they demonstrate proper choices for the parameters of the suggested class of the conjugate gradient methods that may lead to a promising computational performance.