A new sufficient descent conjugate gradient method with exact line search

Abstract

The seminal paper by Hestenes and Stieffel [7] has given rise to an extensive investigation, leading to the development of effective conjugate gradient (CG) methods. In this paper, a new CG algorithm with exact line search which guarantees sufficient descent is proposed. The proposed method is a modified three-term type CG algorithm where the initial search direction is slightly deflected from the currently used Steepest Descent (SD) method. The proposed method is compared with the existing CG methods. These methods were tested using the standard unconstrained optimization functions. Experimental results provide evidence that the proposed method is in general superior to the classical CG methods and has a potential to significantly enhance the computational efficiency and robustness of the optimization method. These algorithms have been carried out by MATLAB R2016a, Intel(R) Core™ i3-7100U CPU @ 2.40GHz RAM 4.GB PC environment.