Variational characterization of the contingent epiderivative

In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of a...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2007-11, Vol.335 (2), p.1374-1382
Main Authors: Rodríguez-Marín, Luis, Sama, Miguel
Format: Article
Language:English
Subjects:
Contingent epiderivative
Exact sciences and technology
Mathematical analysis
Mathematics
Ordered space
Sciences and techniques of general use
Set-valued maps
Variational characterization
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Summary:In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems. When a set-valued map takes values in R n we show that these systems can be formulated in terms of the contingent epiderivatives of scalar set-valued maps. By applying these results we extend some existing theorems.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.01.110