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 Brøndsted-Rockafellar property.

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Keywords

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

Mathematics Subject Classification

47H05; 49J52, 49J53

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Suggested citation

M. Lassonde. “Brøndsted-Rockafellar Property of Subdifferentials of Prox-Bounded Functions.” Journal of Convex Analysis 22 (2015), No. 2, 485–492. https://doi.org/10.68381/jca22022

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.