# 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.
Document type :
Journal articles

https://hal-paris1.archives-ouvertes.fr/hal-01183278
Contributor : Mohammed Bachir <>
Submitted on : Friday, August 7, 2015 - 12:12:35 AM
Last modification on : Thursday, March 5, 2020 - 7:24:16 PM

### Identifiers

• 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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