Fenchel-Moreau conjugation for lower semi-continuous functions

John Cotrina, Elizabeth W. Karas, Ademir A. Ribeiro, Wilfredo Sosa, Jin Y. Yuan

Research output: Contribution to journalArticle in a journalpeer-review

5 Scopus citations


We introduce a modification of Fenchel's conjugation which is a particular case of Moreau's conjugation. We obtain good properties such as convexity of the conjugate function even though the function is not convex. We also introduce the concept of conjugate dual space as a class of continuous operators, while in the Fenchel conjugation the conjugate dual space is the classical topological dual space. Finally, we present some examples for illustrating the difference between the Fenchel-Moreau conjugation and our modification.
Original languageEnglish
Pages (from-to)1045-1057
Number of pages13
Issue number8-9
StatePublished - 1 Aug 2011
Externally publishedYes


  • Fenchel-Moreau conjugate
  • convex function
  • extension of the Fenchel conjugate
  • lower semi-continuous function
  • proper function


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