# Explicit polyhedral approximation of the Euclidean ball

J. Frédéric Bonnans; Marc Lebelle

RAIRO - Operations Research (2010)

- Volume: 44, Issue: 1, page 45-59
- ISSN: 0399-0559

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topFrédéric Bonnans, J., and Lebelle, Marc. "Explicit polyhedral approximation of the Euclidean ball." RAIRO - Operations Research 44.1 (2010): 45-59. <http://eudml.org/doc/250858>.

@article{FrédéricBonnans2010,

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∞ ball,
we discuss the computation of the two first successors, and
give a complete analysis in the case when n=6.
},

author = {Frédéric Bonnans, J., Lebelle, Marc},

journal = {RAIRO - Operations Research},

keywords = {Polyhedral approximation; convex hull; invariance by a group of transformations; canonical cuts; reduction},

language = {eng},

month = {2},

number = {1},

pages = {45-59},

publisher = {EDP Sciences},

title = {Explicit polyhedral approximation of the Euclidean ball},

url = {http://eudml.org/doc/250858},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Frédéric Bonnans, J.

AU - Lebelle, Marc

TI - Explicit polyhedral approximation of the Euclidean ball

JO - RAIRO - Operations Research

DA - 2010/2//

PB - EDP Sciences

VL - 44

IS - 1

SP - 45

EP - 59

AB -
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∞ ball,
we discuss the computation of the two first successors, and
give a complete analysis in the case when n=6.

LA - eng

KW - Polyhedral approximation; convex hull; invariance by a group of transformations; canonical cuts; reduction

UR - http://eudml.org/doc/250858

ER -

## References

top- A. Schrijver, Theory of linear and integer programming. Wiley (1986). Zbl0665.90063
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- A. Ben-Tal and A. Nemirovski, On polyhedral approximations of the second-order cone. Math. Oper. Res.26 (2001) 193–205. Zbl1082.90133
- J.F. Bonnans, Optimisation continue. Dunod, Paris (2006).
- F. Glineur, Computational experiments with a linear approximation of second-order cone optimization. Faculté Polytechnique de Mons (2000). Zbl1204.90117
- J.B. Hiriart-Urruty and M. Pradel, Les boules. Quadrature (2004).
- G. Nemhauser and L. Wolsey, Integer and combinatorial optimization. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons Inc., New York (1999). Reprint of the 1988 original, A Wiley-Interscience Publication.
- G.L. Nemhauser, A.H.G. Rinnoy Kan and M.J. Todd, editors. Optimization, Handbooks in Operations Research and Management Science, Vol. 1, North-Holland, Amsterdam (1989).

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