Clarke’s gradients and epsilon-subgradients in Banach spaces

Treiman, Jay S.

doi:10.1090/S0002-9947-1986-0819935-8

Clarke’s gradients and epsilon-subgradients in Banach spaces
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by Jay S. Treiman

Trans. Amer. Math. Soc. 294 (1986), 65-78

DOI: https://doi.org/10.1090/S0002-9947-1986-0819935-8

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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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A new characterization of Clarke’s tangent cone and its applications to subgradient analysis and optitmization