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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Clarke's gradients and epsilon-subgradients in Banach spaces


Author: Jay S. Treiman
Journal: Trans. Amer. Math. Soc. 294 (1986), 65-78
MSC: Primary 90C48; Secondary 46G05, 49A52, 58C20
MathSciNet review: 819935
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Abstract: A new characterization of Clarke's normal cone to a closed set in a Banach space is given. The normal cone is characterized in terms of weak-star limits of epsilon normals. A similar characterization of Clarke's generalized gradients is also presented. Restrictions must be placed on the Banach spaces to make the formulas valid.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0819935-8
PII: S 0002-9947(1986)0819935-8
Keywords: Nondifferentiable functions, generalized gradients, tangent cones, normal cones
Article copyright: © Copyright 1986 American Mathematical Society