Global Convergence Properties of the HS Conjugate Gradient Method

Copyright c © 2013 Mohammed Belloufi and Rachid Benzine. This is an open access article distributed under the Creative Commons Attribution License, which permits unre-stricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It is well known that global convergence has not been established for the Hestenes-Stiefel (HS) conjugate gradient method using the tra-ditional line searches conditions. In this paper, under some suitable conditions, by using a modified Armijo line search, global convergence results were established for the HS method. Preliminary numerical re-sults on a set of large-scale problems were reported to show that the HS method’s computational effiiciency is encouraging