A Quadratic Hybridization of Polak-RibiSre-Polyak and Fletcher-Reeves Conjugate Gradient Methods

In order to take advantage of the attractive features of Polak-RibiSre-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 Mor,.