TY - JOUR
T1 - A Retrospective Trust Region Algorithm with Trust Region Converging to Zero
AU - Fan , Jinyan
AU - Pan , Jianyu
AU - Song , Hongyan
JO - Journal of Computational Mathematics
VL - 4
SP - 421
EP - 436
PY - 2016
DA - 2016/08
SN - 34
DO - http://doi.org/10.4208/jcm.1601-m2015-0399
UR - https://global-sci.org/intro/article_detail/jcm/9804.html
KW - Retrospective trust region algorithm, Unconstrained optimization, Superlinear
convergence.
AB - <p style="text-align: justify;">We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algorithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.</p>