TY - JOUR
T1 - Curvilinear Paths and Trust Region Methods with Nonmonotonic Back Tracking Technique for Unconstrained Optimization
AU - Zhu , De-Tong
JO - Journal of Computational Mathematics
VL - 3
SP - 241
EP - 258
PY - 2001
DA - 2001/06
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8977.html
KW - Curvilinear paths, Trust region methods,  Nonmonotonic technique, Unconstrained optimization.
AB - <p style="text-align: justify;">In this paper we modify type approximate trust region methods via two curvilinear paths for unconstrained optimization. A mixed strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. We give a series of properties of both optimal path and modified gradient path. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases. &nbsp;</p>