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On measures of size for convex cones

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

Abstract: By using an axiomatic approach we formalize the concept of size index for closed convex cones in the Euclidean space $\mathbb{R}^n$. We review a dozen of size indices disseminated through the literature, commenting on the advantages and disadvantages of each choice.

Keywords: Convex cone, ellipsoidal cone, solid angle, maximal angle, ball-truncated volume, canonical volume, Gaussian width, statistical dimension.

Category 1: Linear, Cone and Semidefinite Programming

Citation: To appear in Journal of Convex Analysis (2015)

Download: [PDF]

Entry Submitted: 05/18/2015
Entry Accepted: 05/18/2015
Entry Last Modified: 05/18/2015

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