Geodesic
Explicit polyhedral approximation of the euclidean ball
RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 1, pp. 45-59

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We discuss the problem of computing points of I Rn 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∞ ball, we discuss the computation of the two first successors, and give a complete analysis in the case when n=6.

DOI : 10.1051/ro/2010003
Classification : 90C05
Keywords: polyhedral approximation, convex hull, invariance by a group of transformations, canonical cuts, reduction 
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     author = {Fr\'ed\'eric Bonnans, J. and Lebelle, Marc},
     title = {Explicit polyhedral approximation of the euclidean ball},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {45--59},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {1},
     year = {2010},
     doi = {10.1051/ro/2010003},
     mrnumber = {2642915},
     zbl = {1188.90167},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2010003/}
}
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Frédéric Bonnans, J.; Lebelle, Marc. Explicit polyhedral approximation of the euclidean ball. RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 1, pp. 45-59. doi: 10.1051/ro/2010003

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