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Epigraphical cones I

Alberto Seeger(alberto.seeger***at***univ-avignon.fr)

Abstract: Up to orthogonal transformation, a solid closed convex cone $K$ in the Euclidean space $\mathbb{R}^{n+1}$ is the epigraph of a nonnegative sublinear function $f:\mathbb{R}^n\to \mathbb{R}$. This work explores the link between the geometric properties of $K$ and the analytic properties of $f$.

Keywords: Convex cone, epigraphical cone, sublinear function, inradius of a cone, solidity, pointedness, angular spectrum

Category 1: Linear, Cone and Semidefinite Programming

Citation: JOURNAL OF CONVEX ANALYSIS, 2011, in press.

Download: [PDF]

Entry Submitted: 01/21/2011
Entry Accepted: 01/21/2011
Entry Last Modified: 01/21/2011

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