Abstract
In this article, a new extension of affine arithmetic is introduced. This technique is based on a quadratic form named general quadratic form. We focus here on the computation of reliable bounds of a function over a hypercube by using this new tool. Some properties of first quadratic functions and then polynomial ones are reported. In order to show the efficiency of such a method, ten polynomial global optimization problems are presented and solved by using an interval branch-and-bound based algorithm.
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The work of the first author was also supported by the Laboratoire de Mathématiques Appliquées CNRS–FRE 2570, Université de Pau et des Pays de l'Adour, France, and by the Laboratoire d'Electrotechnique et d'Electronique Industrielle CNRS–UMR5828, Group EM3, INPT–ENSEEIHT.
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Messine, F., Touhami, A. A General Reliable Quadratic Form: An Extension of Affine Arithmetic. Reliable Comput 12, 171–192 (2006). https://doi.org/10.1007/s11155-006-7217-4
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DOI: https://doi.org/10.1007/s11155-006-7217-4