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A viability approach to the inverse set-valued map theorem
Authors:Jean-Pierre Aubin
Institution:(1) Laboratoire d’Applications des Systémes, Tychastiques Régulés, LASTRE, 14, rue Domat, F-75005 Paris, France
Abstract:The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap.
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