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Titolo:
Limit superior of subdifferentials of uniformly convergent functions
Autore:
Jourani, A;
Indirizzi:
Univ Bourgogne, Lab Anal Appl & Optimisat, F-21011 Dijon, France Univ Bourgogne Dijon France F-21011 l & Optimisat, F-21011 Dijon, France
Titolo Testata:
POSITIVITY
fascicolo: 1, volume: 3, anno: 1999,
pagine: 33 - 47
SICI:
1385-1292(199903)3:1<33:LSOSOU>2.0.ZU;2-E
Fonte:
ISI
Lingua:
ENG
Soggetto:
APPROXIMATE SUBDIFFERENTIALS;
Keywords:
subdifferentials; uniformly convergent functions; Ekeland variational principle; bounded Hausdorff distance; Moreau-Yosida proximal approximation;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
18
Recensione:
Indirizzi per estratti:
Indirizzo: Jourani, A Univ Bourgogne, Lab Anal Appl & Optimisat, BP 400, F-21011 Dijon, France Univ Bourgogne BP 400 Dijon France F-21011 21011 Dijon, France
Citazione:
A. Jourani, "Limit superior of subdifferentials of uniformly convergent functions", POSITIVITY, 3(1), 1999, pp. 33-47

Abstract

In this paper we show that the G - subdifferential of a lower semicontinuous function is contained in the limit superior of the G - subdifferential of lower semicontinuous uniformly convergent family to this function. It happens that this result is equivalent to the corresponding normal cones formulas for family of sets which converges in the sense of the bounded Hausdorff distance. These results extend to the infinite dimensional case those of Ioffe for C-2 - functions and of Benoist for Clarke's normal cone. As an application we characterize the subdifferential of any function which is bounded from below by a negative quadratic form in terms of its Moreau-Yosida proximal approximation.

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Documento generato il 20/09/20 alle ore 22:49:00