A Hybrid PRP-DY Conjugate Gradient with Strong Wolfe-Powell Line Search for Solving Unconstrained Optimization Problem

Abstract

A hybrid conjugate gradient (CG) is one of the iterative methods to enhance the efficiency of the CG methods for solving the large-scale unconstrained optimization problem. CG methods can be practiced in various fields such as engineering, physics and mathematics as it is a simple, straightforward to apply and low memory requirements. Besides, the CG method is easy to understand and superb with numerical performance. Therefore, this paper introduces a hybrid CG method of Polak and Ribière (PRP) and Dai and Yuan (DY) methods, named Akmal, Hamizah and Khadijah (AHK) method. The sufficient descent property and the global convergence of new method is proved under strong Wolfe-Powell line search. Numerical results are represented to show the efficiency of the AHK method by comparing the iteration numbers and the central processing unit (CPU) with other classical and hybrid CG methods. The efficiency of the proposed method is shown by comparing the methods of classicals and hybrids with the AHK method.