Abstract

For an arbitrary non-empty closed convex set A in Rn\mathbb{R}^n, we prove that the polar of the difference between the barrier cone B(A)\mathbb{B}(A) and its interior int⁡(B(A))\operatorname{int}(\mathbb{B}(A)) coincides with the recession cone 0+(cl⁡(G(A)))0^+(\operatorname{cl}(\mathbb{G}(A))) of the closure of the cover G(a)\mathbb{G}(a).

Author information

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

J. Bair

FEGSS, Université de Liège, 7 bd du Rectorat, 4000 Liège, Belgium

J. C. Dupin

Dép. de Mathématiques, Université de Valenciennes, 59304 Valenciennes, France

Keywords

  • Convex set
  • barrier cone
  • recession cone
  • cover
  • polar cone

Mathematics Subject Classification

52A20

Suggested citation

J. Bair, J. C. Dupin. “The Barrier Cone of a Convex Set and the Closure of the Cover.” Journal of Convex Analysis 6 (1999), No. 2, 395–398. https://doi.org/10.68381/jca06024

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Published by Heldermann Verlag, 1999. Rights now held by Banach Press.