A new nonlinear conjugate gradient method

Conjugate gradient (CG) methods are essential for solving large-scale unconstrained optimization problems. Many of studies and modifications have been practiced to improve this method. In this paper, a new class of conjugate gradient coefficients (βk) with a new parameter m = ‖gk‖‖dk−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 step size of CG, denoted as ∝k. Numerical result shows that the new formula is superior and more efficient when compared to other CG coefficients.