New parameter of conjugate gradient method for unconstrained nonlinear optimization

Abstract

We are interested in the performance of nonlinear conjugate gradient methods for unconstrained optimization. Inparticular, we address the conjugate gradient algorithm with strong Wolfe inexact line search. Firstly, we study the descentproperty of the search direction of the considered conjugate gradient algorithm based on a new direction obtained from anew parameter. The main objective of this parameter is to improve the speed of the convergence of the obtained algorithm.Then, we present a complete study that shows the global convergence of this algorithm. Finally, we establish comparativenumerical experiments on well-known test examples to show the efficiency and robustness of our algorithm compared toother recent algorithms.