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Explicit polyhedral approximation of the Euclidean ball

J. Frederic Bonnans 1 M. Lebelle 2 
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We discuss the problem of computing points of IRn whose convex hull contains the Euclidean ball, and is contained in a small multiple of it. Given a polytope containing the Euclidean ball, we introduce its successor obtained by intersection with all tangent spaces to the Euclidean ball, whose normals point towards the vertices of the polytope. Starting from the L-infinity ball, we discuss the computation of the two first successors, and give a complete analysis in the case when n = 6.
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https://hal.inria.fr/inria-00533583
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Submitted on : Sunday, November 7, 2010 - 7:21:37 PM
Last modification on : Saturday, April 23, 2022 - 3:09:31 AM

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J. Frederic Bonnans, M. Lebelle. Explicit polyhedral approximation of the Euclidean ball. RAIRO - Operations Research, EDP Sciences, 2010, 44 (1), pp.45-60. ⟨10.1051/ro/2010003⟩. ⟨inria-00533583⟩

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