Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Ellipsoidal cone
  • Lorentz cone
  • volume of a convex cone
  • cross section
  • axial symmetry
  • semiaxes lengths of an ellipsoidal cone
  • critical angles
  • cone-invariance

Mathematics Subject Classification

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

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Suggested citation

A. Seeger, M. Torki. “Ellipsoidal Cones.” Journal of Convex Analysis 27 (2020), No. 2, 583–622. https://doi.org/10.68381/jca27031

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press LLC.