Abstract

We characterize the closed convex sets K⊂RnK \subset \mathbb{R}^n which satisfy the following approximation condition: for any given point v∈rintKv \in {\rm rint} K and a scalar ε>0\varepsilon > 0, there is a polyhedron P⊂RnP \subset \mathbb{R}^n such that v∈rintPv \in {\rm rint} P and P⊂K⊂v+(1+ε)(P−v)P \subset K \subset v + (1 + \varepsilon)(P - v).

Author information

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Valeriu Soltan

Dept. of Mathematical Sciences, George Mason University, Fairfax, U.S.A.

vsoltan@gmu.edu

Keywords

  • Convex set
  • polyhedron
  • approximation
  • neighborhood
  • homothetic
  • M-decomposable set

Mathematics Subject Classification

52A20, 90C25

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Suggested citation

V. Soltan. “Approximation of Convex Sets by Homothetic Copies of Polyhedra.” Journal of Convex Analysis 33 (2026), No. 1&2, 325–333. https://doi.org/10.68381/jca33020

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.