| Issue |
RAIRO-Oper. Res.
Volume 52, Number 1, January–March 2018
|
|
|---|---|---|
| Page(s) | 177 - 186 | |
| DOI | https://doi.org/10.1051/ro/2018013 | |
| Published online | 23 April 2018 | |
Combination of two underestimators for univariate global optimization
1
LAROMAD, Université Mouloud Mammeri,
Tizi Ouzou, Algeria
2
Laboratoire d’Informatique Theorique Appliquee, IUT de Metz, Université de Lorraine – Metz, Ile du Saulcy,
57045
Metz, France
* Corresponding author: ouanes_mohand@yahoo.fr
Received:
3
March
2017
Accepted:
31
January
2018
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.
Mathematics Subject Classification: 65K05 / 90C30 / 90C34
Key words: Global optimization / αBB method / quadratic underestimator / Branch and Bound
© EDP Sciences, ROADEF, SMAI 2018
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