Convergence Analysis of a New Coefficient Conjugate Gradient Method Under Exact Line Search

Abstract

Conjugate gradient (CG) methods were instrumental in solving unconstrained, wide-ranging optimization. In this paper, we propose a new CG coefficient family, which holds conditions of sufficient descent and global convergence properties. Under exact line search this new CG is evaluated on a set of functions. Based on number of iterations (NOI) and central processing unit (CPU) time, it then compared its output with that of some of the well-known previous CG methods. The results show that of all the methods tested, the latest CG method has the best performance.