# Lower Subdifferentiability and Integration

1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : We consider the question of integration of a multivalued operator $T$, that is the question of finding a function $f$such that $T⊑∂f$. If $∂$ is the Fenchel–Moreau subdifferential, the above problem has been completely solved by Rockafellar, who introduced cyclic monotonicity as a necessary and sufficient condition. In this article we consider the case where $f$ is quasiconvex and $∂$ is the lower subdifferential $∂<$. This leads to the introduction of a property that is reminiscent to cyclic monotonicity. We also consider the question of the density of the domains of subdifferential operators.
Type de document :
Article dans une revue
Set-Valued Analysis, Springer Verlag, 2002, 10 (1), pp.89-108

https://hal-paris1.archives-ouvertes.fr/hal-01183278
Contributeur : Mohammed Bachir <>
Soumis le : vendredi 7 août 2015 - 00:12:35
Dernière modification le : jeudi 11 janvier 2018 - 06:22:32

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• HAL Id : hal-01183278, version 1

### Citation

Mohammed Bachir, Aris Daniilidis, Jean-Paul Penot. Lower Subdifferentiability and Integration. Set-Valued Analysis, Springer Verlag, 2002, 10 (1), pp.89-108. 〈hal-01183278〉

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