The conjugate gradient method is a useful method to solve large-scale unconstrained optimisation problems and to be used in some applications in several fields such as engineering, medical science, image restorations, neural network, and many others. The main benefit of the conjugate gradient method is not using the second derivative or its approximation, such as Newton’s method or its approximation. Moreover, the algorithm of the conjugate gradient method is simple and easy to apply. This study proposes a new modified conjugate gradient method that contains four terms depending on popular two- and three-term conjugate gradient methods. The new algorithm satisfies the descent condition. In addition, the new CG algorithm possesses the convergence property. In the numerical results part, we compare the new algorithm with famous methods such as CG-Descent. We conclude from numerical results that the new algorithm is more efficient than other popular CG methods such as CG-Descent 6.8 in terms of number of function evaluations, number of gradient evaluations, number of iterations, and CPU time.

The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural networks, image restoration, etc. Many complicated methods are proposed to solve these optimization functions in two or three terms. In this paper, we propose a simple, easy, efficient, and robust conjugate gradient method. The new method is constructed based on the Liu and Storey method to overcome the convergence problem and descent property. The new modified method satisfies the convergence properties and the sufficient descent condition under some assumptions. The numerical results show that the new method outperforms famous CG methods such as CG-Descent5.3, Liu and Storey, and Dai and Liao. The numerical results include the number of iterations and CPU time.