Journal of Convex Analysis 22 (2015), No. 2, 485--492
Copyright Heldermann Verlag 2015
Broendsted-Rockafellar Property of Subdifferentials of Prox-Bounded Functions
Marc Lassonde
Université des Antilles et de la Guyane, 97159 Pointe ŕ Pitre, France
marc.lassonde@univ-ag.fr
We provide a new proof that the subdifferential of a proper lower semicontinuous convex function on a Banach space is maximal monotone by adapting the pattern commonly used in the Hilbert setting. We then extend the arguments to show more precisely that subdifferentials of proper lower semicontinuous prox-bounded functions possess the Broendsted-Rockafellar property.
Keywords: Subdifferential, maximal monotonicity, convex function, prox-bounded function, Broendsted-Rockafellar property, variational principle.
MSC: 47H05; 49J52, 49J53
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