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

In this paper, we propose two new dependent Fletcher-Reeves conjugate gradient methods arising from different choice for the scalar βk. We make two different kinds of estimations of upper bounds of ∣βk∣ with respect to βkFR, 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.