In this work, we propose a new underestimator in branch and bound algorithm for solving univariate global optimization problems. The new underestimator is a combination of two underestimators, the classical one used in αBB method (see Androulakis et al. [J. Glob. Optim. 7 (1995) 337–3637]) and the quadratic underestimator developed in Hoai An and Ouanes [RAIRO: OR 40 (2006) 285–302]. We show that the new underestimator is tighter than the two underestimators. A convex/concave test is used to accelerate the convergence of the proposed algorithm. The convergence of our algorithm is shown and a set of test problems given in Casado et al. [J. Glob. Optim. 25 (2003) 345–362] are solved efficiently.
Keywords: Global optimization, αBB method, quadratic underestimator, Branch and Bound
Ouanes, Mohand 1 ; Chebbah, Mohammed 1 ; Zidna, Ahmed 1
@article{RO_2018__52_1_177_0,
author = {Ouanes, Mohand and Chebbah, Mohammed and Zidna, Ahmed},
title = {Combination of two underestimators for univariate global optimization},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {177--186},
year = {2018},
publisher = {EDP Sciences},
volume = {52},
number = {1},
doi = {10.1051/ro/2018013},
mrnumber = {3812475},
zbl = {1397.65090},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2018013/}
}
TY - JOUR AU - Ouanes, Mohand AU - Chebbah, Mohammed AU - Zidna, Ahmed TI - Combination of two underestimators for univariate global optimization JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 177 EP - 186 VL - 52 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2018013/ DO - 10.1051/ro/2018013 LA - en ID - RO_2018__52_1_177_0 ER -
%0 Journal Article %A Ouanes, Mohand %A Chebbah, Mohammed %A Zidna, Ahmed %T Combination of two underestimators for univariate global optimization %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 177-186 %V 52 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2018013/ %R 10.1051/ro/2018013 %G en %F RO_2018__52_1_177_0
Ouanes, Mohand; Chebbah, Mohammed; Zidna, Ahmed. Combination of two underestimators for univariate global optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 177-186. doi: 10.1051/ro/2018013
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