Lower Subdifferentiability and Integration

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.
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https://hal-paris1.archives-ouvertes.fr/hal-01183278
Contributor : Mohammed Bachir <>
Submitted on : Friday, August 7, 2015 - 12:12:35 AM
Last modification on : Sunday, April 7, 2019 - 3:00:03 PM

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  • HAL Id : hal-01183278, version 1

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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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