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
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 |
|---|---|
| Departments | Management |
| Date Deposited | 27 Jan 2011 11:58 |
| URI | https://researchonline.lse.ac.uk/id/eprint/31765 |
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