A Quadratic Hybridization of Polak–Ribière–Polyak and Fletcher–Reeves Conjugate Gradient Methods

In order to take advantage of the attractive features of Polak–Ribière–Polyak and Fletcher–Reeves conjugate gradient methods, two hybridizations of these methods are suggested, using a quadratic relaxation of a hybrid conjugate gradient parameter proposed by Gilbert and Nocedal. In the suggested methods, the hybridization parameter is computed based on a conjugacy condition. Under proper conditions, it is shown that the proposed methods are globally convergent for general objective functions. Numerical results are reported; they demonstrate the efficiency of one of the proposed methods in the sense of the performance profile introduced by Dolan and Moré.