TY - JOUR
T1 - Convergence of Nonlinear Conjugate Gradient Methods
AU -  , Yu-Hong Dai
JO - Journal of Computational Mathematics
VL - 5
SP - 539
EP - 548
PY - 2001
DA - 2001/10
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9006.html
KW - Unconstrained optimization, Conjugate gradient, (generalized) Line search, Global convergence.
AB - <p style="text-align: justify;">This paper proves that a simplified Armijo-type line search can ensure the global convergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for unconstrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.</p>