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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Bachir, M., Daniilidis, A. & Penot, JP. Lower Subdifferentiability and Integration. Set-Valued Analysis 10, 89–108 (2002). https://doi.org/10.1023/A:1014460029093
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DOI: https://doi.org/10.1023/A:1014460029093