In this paper, we propose a new class of adaptive trust region methods for unconstrained optimization problems and develop some convergence properties. In the new algorithms, we use the current iterative information to define a suitable initial trust region radius at each iteration. The initial trust region radius is more reasonable in the sense that the trust region model and the objective function are more consistent at the current iterate. The global convergence, super-linear and quadratic convergence rate are analyzed under some mild conditions. Numerical results show that some special adaptive trust region methods are available and efficient in practical computation.
Mots clés : adaptive trust region method, unconstrained optimization, global convergence, super-linear convergence
@article{RO_2007__41_1_105_0,
author = {Shi, Zhen-Jun and Zhang, Xiang-Sun and Shen, Jie},
title = {Convergence analysis of adaptive trust region methods},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {105--121},
publisher = {EDP-Sciences},
volume = {41},
number = {1},
year = {2007},
doi = {10.1051/ro:2007007},
mrnumber = {2310543},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro:2007007/}
}
TY - JOUR AU - Shi, Zhen-Jun AU - Zhang, Xiang-Sun AU - Shen, Jie TI - Convergence analysis of adaptive trust region methods JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2007 SP - 105 EP - 121 VL - 41 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro:2007007/ DO - 10.1051/ro:2007007 LA - en ID - RO_2007__41_1_105_0 ER -
%0 Journal Article %A Shi, Zhen-Jun %A Zhang, Xiang-Sun %A Shen, Jie %T Convergence analysis of adaptive trust region methods %J RAIRO - Operations Research - Recherche Opérationnelle %D 2007 %P 105-121 %V 41 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro:2007007/ %R 10.1051/ro:2007007 %G en %F RO_2007__41_1_105_0
Shi, Zhen-Jun; Zhang, Xiang-Sun; Shen, Jie. Convergence analysis of adaptive trust region methods. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 1, pp. 105-121. doi : 10.1051/ro:2007007. http://www.numdam.org/articles/10.1051/ro:2007007/
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