Continuity of the Conic Hull

In a real Hilbert space

, the conic hull of

G \subseteq V G ⊆ V

is the set cone

(G) ( G )

consisting of all nonnegative linear combinations of elements of

G G

. Many optimization problems are sensitive to the changes in cone

(G) ( G )

that result from changes in

G G

itself. Motivated by one such problem, we derive necessary and sufficient conditions for the continuity of the conic hull.