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Journal of Convex Analysis 30 (2023), No. 1, 205--216
Copyright Heldermann Verlag 2023

Extreme Points of Convex Sets

Valeriu Soltan
Department of Mathematical Sciences, George Mason University, Fairfax, U.S.A.


\newcommand{\Conv}{\mathrm{conv\,}} \newcommand{\Ext}{\mathrm{ext\,}} \newcommand{\Rec}{\mathrm{rec\,}} \newcommand{\R}{\mathbb{R}} Given a nonempty set $E \subset \R^n$, we provide necessary and sufficient conditions for the existence of a convex set $K \subset \R^n$ (possibly, nonclosed and unbounded) such that $\Ext K = E$. Also, we describe a family of convex sets $K \subset \R^n$ satisfying the equality $K = \Conv (\Ext K)$, and, more general, $K = \Conv (\Ext K) + \Rec K$, where $\Rec K$ denotes the recession cone of $K$.

Keywords: Convex set, convex hull, extreme point, recession cone.

MSC: 52A20, 90C25.

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