Convex Sets and Minimal Sublinear Functions
Amitabh Basu, Gérard Cornuéjols, Giacomo Zambelli · Journal of convex analysis · 2011
We show that, given a closed convex set K K containing the origin in its interior, the support function of the set \{y\in K^* \mid \exists x\in K\text{ such that } \langle x,y \rangle =1\} { y ∈ K ∗ ∣ ∃ x ∈ K such that ⟨ x , y ⟩ = 1 } is the pointwise smallest among all sublinear functions \sigma σ such that K=\{x \mid \sigma(x)\leq 1\} K = { x ∣ σ ( x ) ≤ 1 }