A variant of hybrid conjugate gradient methods based on the convex combination for optimization

Abstract

On some studies a conjugate parameter plays an important role for the conjugate gradient methods. In this paper, a variant of hybrid is provided in the search direction based on the convex combination. This search direction ensures that the descent condition holds. The global convergence of the variant of hybrid is also obtained. Our strong evidence is a numerical analysis showing that the proposed variant of hybrid method is efficient than the Hestenes and Stiefel method.