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 beta(k). We make two different kinds of estimations of upper bounds of vertical bar beta(k)vertical bar with respect to beta(FR)(k), 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. (c) 2006 Elsevier Inc. All rights reserved.