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

 

Submonotone subdifferentials of Lipschitz functions


Author: Jonathan E. Spingarn
Journal: Trans. Amer. Math. Soc. 264 (1981), 77-89
MSC: Primary 26B25; Secondary 47H05, 49A51, 58C20, 90C25
MathSciNet review: 597868
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0597868-8
PII: S 0002-9947(1981)0597868-8
Keywords: Submonotone mapping, generalized gradient, lower-$ {C^1}$ function, nondifferentiable optimization
Article copyright: © Copyright 1981 American Mathematical Society