English

Convex Sets and Minimal Sublinear Functions

Metric Geometry 2017-01-24 v1 Optimization and Control

Abstract

We show that, given a closed convex set KK containing the origin in its interior, the support function of the set {yK:xK\mboxsuchthatx,y=1}\{y\in K^*: \exists x\in K\mbox{ 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: \sigma(x)\leq 1\}.

Cite

@article{arxiv.1701.06550,
  title  = {Convex Sets and Minimal Sublinear Functions},
  author = {Amitabh Basu and Gerard Cornuejols and Giacomo Zambelli},
  journal= {arXiv preprint arXiv:1701.06550},
  year   = {2017}
}
R2 v1 2026-06-22T17:57:38.485Z