A convex combination of improved Fletcher-Reeves and Rivaie-Mustafa-Ismail-Leong conjugate gradient methods for unconstrained optimization problems and applications

Abstract

Conjugate gradient methods are probably the most used methods in solving large scale unconstrained optimization problems. They have become popular because of their simplicity and low memory requirements. In this paper, we propose a hybrid conjugate gradient method based on the improved Fletcher-Reeves (IFR) and Rivaie-Mustafa-Ismail-Leong+ (RMIL+) methods and establish its global convergence under the strong Wolfe line search conditions. The new conjugate gradient direction satisfies the sufficient descent condition. The method is then compared to other methods in the literature and numerical experiments show that it is competent when solving large scale unconstrained optimization problems. Furthermore, the method is applied to solve a problem in portfolio selection.