TY - JOUR
T1 - A New Nonmonotone Trust Region Algorithm for Solving Unconstrained Optimization Problems
AU - Jinghui Liu & Changfeng Ma
JO - Journal of Computational Mathematics
VL - 4
SP - 476
EP - 490
PY - 2014
DA - 2014/08
SN - 32
DO - http://doi.org/10.4208/jcm.1401-m3975
UR - https://global-sci.org/intro/article_detail/jcm/9898.html
KW - Unconstrained optimization problems, nonmonotone trust region method, global convergence, superlinear convergence.
AB - <p style="text-align: justify;">Based on the nonmonotone line search technique proposed by Gu and Mo (Appl. Math. Comput. 55, (2008) pp. 2158-2172), a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio $ρ_k$ for evaluating the trial step $d_k$ whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.</p>