Open AccessGlobal convergence properties of the HS conjugate gradient method
Author(s) -
Mohammed Belloufi,
Rachid Benzine
Publication year - 2013
Publication title -
applied mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 1314-7552
pISSN - 1312-885X
DOI - 10.12988/ams.2013.311638
Subject(s) - conjugate gradient method , convergence (economics) , derivation of the conjugate gradient method , mathematics , conjugate , conjugate residual method , nonlinear conjugate gradient method , computer science , mathematical optimization , mathematical analysis , gradient descent , artificial intelligence , economics , artificial neural network , economic growth
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.
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