Journal of Convex Analysis 19 (2012), No. 1, 001--021
Copyright Heldermann Verlag 2012
Epigraphical Cones II
University of Avignon, Dept. of Mathematics, 33 rue Louis Pasteur, 84000 Avignon, France
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 is an epigraphical cone if it can be represented as epigraph of a nonnegative sublinear function f from Rn to R. We explore the link between the geometric properties of K and the analytic properties of f.
Keywords: Convex cone, epigraphical cone, sublinear function, smoothness, rotundity, Vinberg characteristic function, conic programming.
MSC: 46B10, 46B20, 52A41
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