Journal of convex analysis, Tome 18 (2011) no. 2, pp. 427-432
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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/
@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/}
}
TY - JOUR
AU - A. Basu
AU - G. Cornuéjols
AU - G. Zambelli
TI - Convex Sets and Minimal Sublinear Functions
JO - Journal of convex analysis
PY - 2011
SP - 427
EP - 432
VL - 18
IS - 2
UR - http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a9/
ID - JCA_2011_18_2_JCA_2011_18_2_a9
ER -
%0 Journal Article
%A A. Basu
%A G. Cornuéjols
%A G. Zambelli
%T Convex Sets and Minimal Sublinear Functions
%J Journal of convex analysis
%D 2011
%P 427-432
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a9/
%F JCA_2011_18_2_JCA_2011_18_2_a9
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 $K=\{x \mid \sigma(x)\leq 1\}$.
