TY - JOUR
T1 - A globally convergent Polak-Ribière-Polyak conjugate gradient method with Armijo-type line search
AU - G. Yu, L. Guan & Z. Wei 
JO - Numerical Mathematics, a Journal of Chinese Universities
VL - 4
SP - 357
EP - 366
PY - 2006
DA - 2006/11
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nm/8042.html
KW - 
AB - 
In this paper, we propose a globally convergent
Polak-Ribi\`{e}re-Polyak (PRP) conjugate gradient method for
nonconvex minimization of differentiable functions by employing an
Armijo-type line search which is simpler and less demanding than
those defined in [4,10]. A favorite property of this method is that
we can
 choose the initial stepsize as the one-dimensional minimizer of a quadratic model
$\Phi(t):=f(x_k)+t g_k^Td_k+\frac{1}{2}t^2d_k^TQ_kd_k$, where $Q_k$
is a positive definite matrix that carries some second order
information of the objective function $f$. So, this line search may
make the stepsize $t_k$ more easily accepted.
 Preliminary numerical results show that this
method is efficient.