A New Coefficient of the Conjugate Gradient Method with the Sufficient Descent Condition and Global Convergence Properties

Conjugate gradient methods are the most famous methods for solving unconstrained, large-scale optimization. In this article, we propose a new coefficient of the conjugate gradient method for solving unconstrained minimization problems. The new method is a modification of NPRP (2009) coefficient. The sufficient descent condition and global convergence of the new method are given under the exact line search and the strong Wolfe line search with sigma is an element of (0, 1/8). The numerical results show that the new method has good performance in solving unconstrained minimization problems.