Abstract

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

Author information

Contact details are reproduced from the original publication and may be historical.

Valeriu Soltan

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

vsoltan@gmu.edu

Keywords

  • Convex set
  • convex hull
  • extreme point
  • recession cone

Mathematics Subject Classification

52A20, 90C25

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Suggested citation

V. Soltan. “Extreme Points of Convex Sets.” Journal of Convex Analysis 30 (2023), No. 1, 205–216. https://doi.org/10.68381/jca30012

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Published by Heldermann Verlag, 2023. Rights now held by Banach Press.