A new hybrid conjugate gradient method as a convex combination of HZ and FR and PRP methods

Abstract

In this paper, we propose a new conjugate gradient method for solving
unconstrained optimization problem, whom is convex combination of the
Hager-Zhan, Fletcher-Reeves and Polak-Rib\'{e}re-Polyak algorithms. The
search direction satisfies the sufficient descent condition and guarantees
global convergence under the strong Wolfe line search conditions. Moreover,
several numerical experiments on standard test functions are presented to
illustrate that the proposed method is efficient and competitive compared to
existing conjugate gradient methods.