Upper Bounding in Inner Regions for Global Optimization under Inequality Constraints

Ignacio Araya 1 Gilles Trombettoni 2 Bertrand Neveu 3, 4, 5 Gilles Chabert 6, 7
2 COCONUT - Agents, Apprentissage, Contraintes
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
5 IMAGINE [Marne-la-Vallée]
LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech
7 TASC - Theory, Algorithms and Systems for Constraints
Inria Rennes – Bretagne Atlantique , Département informatique - EMN, LINA - Laboratoire d'Informatique de Nantes Atlantique
Abstract : In deterministic continuous constrained global optimization, upper bounding the objective function generally resorts to local minimization at several nodes/iterations of the branch and bound. We propose in this paper an alternative approach when the constraints are inequalities and the feasible space has a non-null volume. First, we extract an inner region , i.e., an entirely feasible convex polyhedron or box in which all points satisfy the constraints. Second, we select a point inside the extracted inner region and update the upper bound with its cost. We describe in this paper two original inner region extraction algorithms implemented in our interval B&B called IbexOpt. They apply to nonconvex constraints involving mathematical operators like +,x,power,sqrt,exp,log,sin. This upper bounding shows very good performance obtained on medium-sized systems proposed in the COCONUT suite.
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Submitted on : Monday, September 8, 2014 - 12:08:26 PM
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Ignacio Araya, Gilles Trombettoni, Bertrand Neveu, Gilles Chabert. Upper Bounding in Inner Regions for Global Optimization under Inequality Constraints. Journal of Global Optimization, Springer Verlag, 2014, 60 (2), pp.145-164. ⟨10.1007/s10898-014-0145-7⟩. ⟨hal-01061701⟩



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