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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Tangent cones and quasi-interiorly tangent cones to multifunctions

Author: Lionel Thibault
Journal: Trans. Amer. Math. Soc. 277 (1983), 601-621
MSC: Primary 58C20; Secondary 26E25, 90C30
MathSciNet review: 694379
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Abstract: R. T. Rockafellar has proved a number of rules of subdifferential calculus for nonlocally lipschitzian real-valued functions by investigating the Clarke tangent cones to the epigraphs of such functions. Following these lines we study in this paper the tangent cones to the sum and the composition of two multifunctions. This will be made possible thanks to the notion of quasi-interiorly tangent cone which has been introduced by the author for vector-valued functions in [29] and whose properties in the context of multifunctions are studied. The results are strong enough to cover the cases of real-valued or vector-valued functions.

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Keywords: Tangent cones, quasi-interiorly tangent cones, convex and lipschitzian multifunctions, additively separate multifunctions
Article copyright: © Copyright 1983 American Mathematical Society