Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Subdifferential
  • maximal monotonicity
  • convex function
  • prox-bounded function
  • Broendsted-Rockafellar property
  • variational principle

Mathematics Subject Classification

47H05; 49J52, 49J53

Suggested citation

M. Lassonde. “Broendsted-Rockafellar Property of Subdifferentials of Prox-Bounded Functions.” Journal of Convex Analysis 22 (2015), No. 2, 485–492.

Copyright Heldermann Verlag 2015