Abstract

In a real Hilbert space VV, the conic hull of G⊆VG \subseteq V is the set cone (G)(G) consisting of all nonnegative linear combinations of elements of GG. Many optimization problems are sensitive to the changes in cone (G)(G) that result from changes in GG itself. Motivated by one such problem, we derive necessary and sufficient conditions for the continuity of the conic hull.

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Keywords

  • Cone
  • conic hull
  • positive hull
  • continuity
  • maximal angle

Mathematics Subject Classification

90C31, 90C26, 52B55

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Suggested citation

M. Orlitzky. “Continuity of the Conic Hull.” Journal of Convex Analysis 31 (2024), No. 1, 255–264. https://doi.org/10.68381/jca31015

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.