Journal of Convex Analysis 33 (2026), No. 1&2, 325--333
Copyright Heldermann Verlag 2026
Approximation of Convex Sets by Homothetic Copies of Polyhedra
Valeriu Soltan
Dept. of Mathematical Sciences, George Mason University, Fairfax, U.S.A.
vsoltan@gmu.edu
[Abstract-pdf]
We characterize the closed convex sets $K \subset \mathbb{R}^n$ which satisfy the following approximation condition: for any given point $v \in {\rm rint} K$ and a scalar $\varepsilon > 0$, there is a polyhedron $P \subset \mathbb{R}^n$ such that $v \in {\rm rint} P$ and $P \subset K \subset v + (1 + \varepsilon)(P - v)$.
Keywords: Convex set, polyhedron, approximation, neighborhood, homothetic, M-decomposable set.
MSC: 52A20, 90C25.
[ Fulltext-pdf (100 KB)] for subscribers only.