Global convergence properties of the HS conjugate gradient method

Mohammed Belloufi, Rachid Benzine
2013 Applied Mathematical Sciences  
It is well known that global convergence has not been established for the Hestenes-Stiefel (HS) conjugate gradient method using the traditional 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 results on a set of large-scale problems were reported to show that the HS method's computational effiiciency is encouraging. Mathematics Subject
more » ... Subject Classification: 90C06; 90C30; 65K05
doi:10.12988/ams.2013.311638 fatcat:btmccz2eabaulh3taph3y7krve