A modified Conjugate Gradient method with Sufficient Condition and Conjugacy Condition

Abstract

Nonlinear conjugate gradient methods are significant for solving large-scale unconstrained optimization problems

Nonlinear conjugate gradient methods are significant for solving large-scale unconstrained optimization problems. Several studies and modifications have been carried out to improve this method. The strong Wolfe line search is usually used in practice for analyzing and implementing conjugate gradient methods. In this paper, a little modification to conjugate descent method was presented for unconstrained optimization. The proposed method satisfies the descent condition and the famous D-L conjugacy condition. Furthermore, the sufficient decent condition and global convergence result are established using strong Wolfe line search. Numerical result shows that this formula of conjugate gradient is more robust and effective.