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 large-scale unconstrained optimization problems. Many studies and modifications have been conducted recently to improve this method. In this paper, a new class of conjugate gradient coefficients (βk) with a new parameter m=‖gk‖/‖gk−1‖ that possess global convergence properties is presented. The global convergence and sufficient decent property result is established using inexact line searches to determine the (αk>0) is a step size of CG methods. Numerical result shows that the new formula is superior and more efficient when compared to other CG coefficients.