A Descent Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems with Application

Abstract

In recent years, there has been a surge of attention to the Conjugate Gradient Method (CGM) and its applications. This is because the algorithm of CGM does not require the computation of the second derivative or an approximation during the iteration process. In this study, a four-term descent CGM is proposed by utilizing the famous Polak–Ribiere–Polyak (PRP) conjugate gradient formula. The direction of the proposed method achieves the descent property without line search consideration. In addition, the convergence properties are met to generate the stationary points. Findings from numerical experiments on unconstrained optimization and robotic motion control problems demonstrate that the novel approach outperforms some existing methods including the famous CG-Descent conjugate gradient method.