A new conjugate gradient method with exact line search - Mustafa, Mamat; Mohd, Rivaie; Syazni, Shoid (HIKARI Ltd., 2015)
Conjugate gradient (CG) methods have been practically used to solve large-scale unconstrained optimization problems due to their simplicity and low memory storage. In this paper, we proposed a new type of CG coefficients ( )  k . The  k is computed as an average between two different types of method which are Polak and Ribiere (PR) and Norrlaili et al. (NRMI). Numerical comparisons are made with the five others  k proposed by the early researches. A set of eight unconstrained optimization problems with several different variables are used in this paper. It is shown that, the new proposed  k with an exact line search is possessed global convergence properties. Numerical results also show that this new  k outperforms some of these CG methods.