A Contractor Based on Convex Interval Taylor

Abstract : Interval Taylor has been proposed in the sixties by the interval analysis community for relaxing non-convex continuous constraint systems. However, it generally produces a non-convex relaxation of the solution set. A simple way to build a convex polyhedral relaxation is to select a corner of the studied domain/box as expansion point of the interval Taylor form, instead of the usual midpoint. The idea has been proposed by Neumaier to produce a sharp range of a single function and by Lin and Stadtherr to handle n * n (square) systems of equations. This paper presents an interval Newton-like operator, called X-Newton, that iteratively calls this interval convexification based on an endpoint interval Taylor. This general-purpose contractor uses no preconditioning and can handle any system of equality and inequality constraints. It uses Hansen's variant to compute the interval Taylor form and uses two opposite corners of the domain for every constraint. The X-Newton operator can be rapidly encoded, and produces good speedups in constrained global optimization and non-convex constraint satisfaction. First experiments compare X-Newton with affine arithmetic.
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Contributeur : Gilles Trombettoni <>
Soumis le : jeudi 23 février 2012 - 19:09:14
Dernière modification le : mercredi 11 avril 2018 - 12:12:03
Document(s) archivé(s) le : vendredi 23 novembre 2012 - 14:31:14


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  • HAL Id : hal-00673447, version 1


Ignacio Araya, Gilles Trombettoni, Bertrand Neveu. A Contractor Based on Convex Interval Taylor. [Research Report] RR-7887, INRIA. 2012, pp.23. 〈hal-00673447〉



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