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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.

Gérard Cornuéjols
Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 12180, U.S.A.

Giacomo Zambelli
Dept. of Management, London School of Economics, Houghton Street, London WC2A 2AE, England


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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