Integration formulas via the Fenchel subdifferential of nonconvex functions

Rafael Correa, Yboon García, Abderrahim Hantoute

Research output: Contribution to journalArticle in a journalpeer-review

16 Scopus citations


Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the ε- subdifferential and the Fenchel subdifferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction of the lsc convex envelope either in terms of the ε-subdifferential of the nominal function or of the subdifferential of its weak lsc envelope.
Original languageEnglish
Pages (from-to)1188-1201
Number of pages14
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number3
StatePublished - 1 Feb 2012


  • Conjugate function
  • Epi-pointed functions
  • Integration
  • Lower semicontinuous convex envelope
  • ε-subdifferential


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