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Journal of Convex Analysis 31 (2024), No. 1, 255--264
Copyright Heldermann Verlag 2024

Continuity of the Conic Hull

Michael Orlitzky
University of Maryland Baltimore County, Baltimore, U.S.A.


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

Keywords: Cone, conic hull, positive hull, continuity, maximal angle.

MSC: 90C31, 90C26, 52B55.

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