Global convergence properties of the two new dependent Fletcher–Reeves conjugate gradient methods

Abstract

In this paper, we propose two new dependent Fletcher–Reeves conjugate gradient methods arising from different choice for the scalar β k . We make two different kinds of estimations of upper bounds of ∣ β k ∣ with respect to β k FR , which are based on Abel Theorem of non-convergent series of positive items. With several different line searches, global convergence results are established for the two new methods which extend the previous dependent Fletcher–Reeves conjugate gradient methods.