Differentiable Selections of Set-Valued Mappings

Darinka Dentcheva
We consider set-valued mappings defined on a linear normed space with convex closed images in IRn. Our aim is to construct selections which are (Hadamard) directionally differentiable using some approximation of the multifunction. The constructions suggested assume existence of a cone approximation given by a certain “derivative” of the mapping. The first one makes use of the properties of Steiner points. The notion of Steiner center is generalized for a class of unbounded sets, which...
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