Journal of Convex Analysis 18 (2011), No. 2, 427--432
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
[Abstract-pdf]
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 $K=\{x \mid \sigma(x)\leq 1\}$.
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