A New Coefficient of Conjugate Gradient Method with Global Convergence for Unconstrained Optimization Problems

In this article, we defined a new coefficient formula of the conjugate gradient method for solving non linear unconstrained optimization problems. The new formula β new k is type of line search and the idea of our work is to focus on modification the Perry’s suggestion. We further show that global convergence result of new formula is recognized under Wolf-Powell line search. It is shown that the new CG coefficient satisfied sufficient descent conditions. In the end, numerical experiments with the collection of test functions show that the new β new k is more effective compared to some other standard formulas such as β H−S k , β Perry k and β D−Y k .