# Convex Sets and Minimal Sublinear Functions

Basu, Amitabh , Cornuéjols, Gérard and Zambelli, Giacomo (2011) Convex Sets and Minimal Sublinear Functions. Journal of Convex Analysis, 18 (2). pp. 427-432. ISSN 0944-6532

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## Abstract

We show that, given a closed convex set $K$ containing the origin in its interior, the support function of the set $\{y\in K^* \mid \mbox{ there exists } x\in K\mbox{ such that } \langle x,y \rangle =1\}$ is the pointwise smallest among all sublinear functions $\sigma$ such that $K=\{x \mid \sigma(x)\leq 1\}$.

Item Type: Article http://www.heldermann.de/ © 2011 Heldermann Verlag Q Science > QA Mathematics Departments > Management http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx 27 Jan 2011 11:58 http://eprints.lse.ac.uk/31765/