
Journal of Convex Analysis 18 (2011), No. 2, 427432 Copyright Heldermann Verlag 2011 Convex Sets and Minimal Sublinear Functions Amitabh Basu Dept. of Mathematics, University of California, One Shields Avenue, Davis, CA 95616, U.S.A. abasu@math.ucdavis.edu Gérard Cornuéjols Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 12180, U.S.A. gc0v@andrew.cmu.edu Giacomo Zambelli Dept. of Management, London School of Economics, Houghton Street, London WC2A 2AE, England g.zambelli@lse.ac.uk [Abstractpdf] 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 $K=\{x \mid \sigma(x)\leq 1\}$. [ Fulltextpdf (106 KB)] for subscribers only. 