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Transactions of the American Mathematical Society

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Regular points of Lipschitz functions


Author: Alexander D. Ioffe
Journal: Trans. Amer. Math. Soc. 251 (1979), 61-69
MSC: Primary 58E15; Secondary 49B99
MathSciNet review: 531969
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Abstract: Let f be a locally Lipschitz function on a Banach space X, and S a subset of X. We define regular (i.e. noncritical) points for f relative to S, and give a sufficient condition for a point $ z \, \in \, S$ to be regular. This condition is then expressed in the particular case when f is $ {C^1}$, and is used to obtain a new proof of Hoffman's inequality in linear programming.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0531969-6
Article copyright: © Copyright 1979 American Mathematical Society