A modified nonlinear conjugate gradient method for unconstrained optimization

Abstract

Nonlinear conjugate gradient method holds an important role in solving large scale unconstrained optimization problems. Their simplicity, low memory requirement, and global convergence stimulated a massive study on the method. Numerous modifications have been done recently to improve its performance. In this paper, we proposed a new formula for the conjugate gradient coefficient k  that generates the descent search direction. In addition, we establish the global convergence result under exact line search. The outcome of our numerical experiment show that the proposed formula is very efficient and more reliable when compare to other conjugate gradient methods.