Abstract

We show that, given a closed convex set KK containing the origin in its interior, the support function of the set {y∈K∗∣∃x∈K such that ⟨x,y⟩=1}\{y\in K^* \mid \exists x\in K\text{ such that } \langle x,y \rangle =1\} is the pointwise smallest among all sublinear functions σ\sigma such that K={x∣σ(x)≤1}K=\{x \mid \sigma(x)\leq 1\}

Author information

Contact details are reproduced from the original publication and may be historical.

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

Suggested citation

A. Basu, G. Cornuéjols, G. Zambelli. “Convex Sets and Minimal Sublinear Functions.” Journal of Convex Analysis 18 (2011), No. 2, 427–432. https://doi.org/10.68381/jca18026

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press.