Abstract

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

Copyright Heldermann Verlag 1999