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Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint

Published online by Cambridge University Press:  08 November 2006

Hoai An Le Thi  and
Mohand Ouanes
Hoai An Le Thi
Affiliation:
Laboratoire de l'Informatique Théorique et Appliquée, UFR Scientifique MIM Université Paul Verlaine – Metz, Ile du Saulcy, 57045 Metz, France; [email protected]
Mohand Ouanes
Affiliation:
Laboratoire de l'Informatique Théorique et Appliquée, UFR Scientifique MIM Université Paul Verlaine – Metz, Ile du Saulcy, 57045 Metz, France; [email protected] Département de Mathématiques, Faculté des Sciences, Université de Tizi-Ouzou, Algeria.
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Abstract

The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems withboth twice differentiable function and constraint, we can propose an efficientalgorithm based on Branch and Bound techniques. The method is firstdisplayed in the simple case with an interval constraint. The extension is displayedafterwards to the general case with an additional nonconvex twicedifferentiable constraint. A quadratic bounding function which is betterthan the well known linear underestimator is proposed while w-subdivision is added to support the branching procedure. Computational results on several andvarious types of functions show the efficiency of our algorithms and theirsuperiority with respect to the existing methods.

Keywords

Global optimizationbranch and boundquadraticunderestimationw-subdivision.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 3 , July 2006 , pp. 285 - 302
Copyright
© EDP Sciences, 2006

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