Article ID: | iaor20123762 |
Volume: | 60 |
Issue: | 1 |
Start Page Number: | 135 |
End Page Number: | 152 |
Publication Date: | May 2012 |
Journal: | Numerical Algorithms |
Authors: | Zhang Yang, Wang Kairong |
Keywords: | gradient methods |
Although the study of global convergence of the Polak–Ribière–Polyak (PRP), Hestenes–Stiefel (HS) and Liu–Storey (LS) conjugate gradient methods has made great progress, the convergence of these algorithms for general nonlinear functions is still erratic, not to mention under weak conditions on the objective function and weak line search rules. Besides, it is also interesting to investigate whether there exists a general method that converges under the standard Armijo line search for general nonconvex functions, since very few relevant results have been achieved. So in this paper, we present a new general form of conjugate gradient methods whose theoretical significance is attractive. With any formula