Abstract

This is the second part of a work devoted to the theory of epigraphical cones and their applications. For part one see this journal 18 (2011) 1171–1196. A convex cone K in the Euclidean space Rn+1\mathbb{R}^{n+1} is an epigraphical cone if it can be represented as epigraph of a nonnegative sublinear function f from Rn\mathbb{R}^n to R\mathbb{R}. We explore the link between the geometric properties of K and the analytic properties of f.

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Keywords

  • Convex cone
  • epigraphical cone
  • sublinear function
  • smoothness
  • rotundity
  • Vinberg characteristic function
  • conic programming

Mathematics Subject Classification

46B10, 46B20, 52A41

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Suggested citation

A. Seeger. “Epigraphical Cones II.” Journal of Convex Analysis 19 (2012), No. 1, 1–21. https://doi.org/10.68381/jca19001

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.