Bounded linear regularity of convex sets in Banach spaces and its applications

Abstract.This paper deals with bounded linear regularity, linear regularity and the strong conical hull intersection property (CHIP) of a collection of finitely many closed convex intersecting sets in Banach spaces. It is shown that, as in finite dimensional space setting (see [6]), the standard constraint qualification implies bounded linear regularity, which in turn yields the strong conical hull intersection property, and that the collection of closed convex sets {C1, . . . ,Cn} is bounded linearly regular if and only if the tangent cones of {C1, . . . ,Cn} has the CHIP and the normal cones of {C1, . . . ,Cn} has the property (G)(uniformly on a neighborhood in the intersection C). As applications, we study the global error bounds for systems of linear and convex inequalities.

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