Global convergence analysis of a new nonlinear conjugate gradient coefficient with strong wolfe line search

Abstract

Nonlinear conjugate gradient (CG) methods are the most important method for solving largescale unconstrained optimisation problems. Many studies and modifications have been conducted recently to improve this method. In this paper, a new class of conjugate gradient coefficients β k with a new parameter m = gk gk−1 that possesses global convergence properties is presented. The global convergence and sufficient descent property is established using inexact line searches to determine that α k is the step size of CG methods. Numerical result shows that the new formula is superior and more efficient when compared to other CG coefficients.