A descent hybrid modification of the Polak–Ribière–Polyak conjugate gradient method

¹ Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195–363, Semnan, Iran.
sbk@semnan.ac.ir
² Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box: 9177948953, Mashhad, Iran.
rghanbari@um.ac.ir

Received: 10 August 2015
Accepted: 26 January 2016

Abstract

Hybridizing self-adjusting approach of Dong et al. and three-term formulation of Zhang et al., a nonlinear conjugate gradient method is proposed. The method reduces to the Polak–Ribière–Polyak method under the exact line search and satisfies the sufficient descent condition independent of the line search and the objective function convexity. Similar to the Polak–Ribière–Polyak method, the method possesses an automatic restart feature which avoids jamming. Global convergence analyses are conducted when the line search fulfills the popular Wolfe conditions as well as an Armijo-type condition. Numerical experiments are done on a set of CUTEr unconstrained optimization test problems. Results of comparisons show computational efficiency of the proposed method in the sense of Dolan–Moré performance profile.