Based on a modified secant equation, we propose a scalar approximation of the Hessian to be used in the trust region subproblem. Then, we suggest an adaptive nonmonotone trust region algorithm with a simple quadratic model. Under proper conditions, it is briefly shown that the proposed algorithm is globally and locally superlinearly convergent. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection, using the Dolan-Moré performance profile. They demonstrate efficiency of the proposed algorithm.
Mots-clés : Unconstrained optimization, trust region method, secant equation, adaptive radius, global convergence, superlinear convergence
@article{RO_2019__53_3_829_0,
author = {Rezaee, Saeed and Babaie-Kafaki, Saman},
title = {An adaptive nonmonotone trust region method based on a modified scalar approximation of the {Hessian} in the successive quadratic subproblems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {829--839},
publisher = {EDP-Sciences},
volume = {53},
number = {3},
year = {2019},
doi = {10.1051/ro/2017057},
zbl = {1461.65182},
mrnumber = {3973925},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2017057/}
}
TY - JOUR AU - Rezaee, Saeed AU - Babaie-Kafaki, Saman TI - An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 829 EP - 839 VL - 53 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2017057/ DO - 10.1051/ro/2017057 LA - en ID - RO_2019__53_3_829_0 ER -
%0 Journal Article %A Rezaee, Saeed %A Babaie-Kafaki, Saman %T An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 829-839 %V 53 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2017057/ %R 10.1051/ro/2017057 %G en %F RO_2019__53_3_829_0
Rezaee, Saeed; Babaie-Kafaki, Saman. An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 3, pp. 829-839. doi : 10.1051/ro/2017057. http://www.numdam.org/articles/10.1051/ro/2017057/
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