Geodesic
Convex Sets and Minimal Sublinear Functions
Journal of convex analysis, Tome 18 (2011) no. 2, pp. 427-432
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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 $K=\{x \mid \sigma(x)\leq 1\}$. 
@article{JCA_2011_18_2_JCA_2011_18_2_a9,
     author = {A. Basu and G. Cornu\'ejols and G. Zambelli},
     title = {Convex {Sets} and {Minimal} {Sublinear} {Functions}},
     journal = {Journal of convex analysis},
     pages = {427--432},
     year = {2011},
     volume = {18},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a9/}
}
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A. Basu; G. Cornuéjols; G. Zambelli. Convex Sets and Minimal Sublinear Functions. Journal of convex analysis, Tome 18 (2011) no. 2, pp. 427-432. http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a9/