Geodesic
Extreme Points of Convex Sets
Journal of convex analysis, Tome 30 (2023) no. 1, pp. 205-216
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\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 $K$.
Classification : 52A20, 90C25
Mots-clés : Convex set, convex hull, extreme point, recession cone 
@article{JCA_2023_30_1_JCA_2023_30_1_a11,
     author = {V. Soltan},
     title = {Extreme {Points} of {Convex} {Sets}},
     journal = {Journal of convex analysis},
     pages = {205--216},
     year = {2023},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a11/}
}
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V. Soltan. Extreme Points of Convex Sets. Journal of convex analysis, Tome 30 (2023) no. 1, pp. 205-216. http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a11/