Geodesic
Combination of two underestimators for univariate global optimization
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 177-186

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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.

DOI : 10.1051/ro/2018013
Classification : 65K05, 90C30, 90C34
Keywords: Global optimization, αBB method, quadratic underestimator, Branch and Bound

Ouanes, Mohand 1 ; Chebbah, Mohammed 1 ; Zidna, Ahmed 1

1 
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     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},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {1},
     year = {2018},
     doi = {10.1051/ro/2018013},
     mrnumber = {3812475},
     zbl = {1397.65090},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2018013/}
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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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