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Journal Articles Set-Valued Analysis Year : 2002

## Lower Subdifferentiability and Integration

Mohammed Bachir
• Function : Author
• PersonId : 960537
Aris Daniilidis
• Function : Author
• PersonId : 843792
Jean-Paul Penot
• Function : Author
• PersonId : 842952

#### 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.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-01183278 , version 1 (07-08-2015)

### Identifiers

• HAL Id : hal-01183278 , version 1

### Cite

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

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