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Journal of Convex Analysis 27 (2020), No. 2, 583--622
Copyright Heldermann Verlag 2020

Ellipsoidal Cones

Alberto Seeger
Dép. de Mathématiques, Université d'Avignon, 84000 Avignon, France

Mounir Torki
CERI, Université d'Avignon, 84911 Avignon, France

Ellipsoidal cones are more general than revolution cones but they still have a simple structure. Such a compromise between simplicity and sufficient degree of generality make them very useful in practice. Ellipsoidal cones have applications in optimization, statistics, control of linear dynamical systems, and in many other fields. The purpose of this survey paper is to gather in a single place a rich variety of results on ellipsoidal cones disseminated in the literature. A few selected examples of applications are provided to show the importance of this particular class of convex cones.

Keywords: Ellipsoidal cone, Lorentz cone, volume of a convex cone, cross section, axial symmetry, semiaxes lengths of an ellipsoidal cone, critical angles, cone-invariance.

MSC: 15A18, 15A63, 52A20, 52A38, 52A40

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