Submonotone subdifferentials of Lipschitz functions

Spingarn, Jonathan E.

doi:10.1090/S0002-9947-1981-0597868-8

Submonotone subdifferentials of Lipschitz functions
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by Jonathan E. Spingarn

Trans. Amer. Math. Soc. 264 (1981), 77-89

DOI: https://doi.org/10.1090/S0002-9947-1981-0597868-8

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Abstract:

The class of "lowwer-${C^1}$" functions, that is functions which arise by taking the maximum of a compactly indexed family of ${C^1}$ functions, is characterized in terms of properties of the generalized subdifferential. A locally Lipschitz function is shown to be lower-${C^1}$ if and only if its subdifferential is "strictly submonotone". Other properties of functions with "submonotone" subdifferentials are investigated.

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The theory of subgradients and its applications to problems of optimization