Comparing Fenchel-Moreau conjugates with level set conjugates

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Abstract

We compare the Fenchel-Moreau second conjugates associated to an arbitrary coupling function φ: X × W → R̄ = [-∞, + ∞] between two sets X and W with the second level set conjugates associated to the same coupling. For a coupling φ: Rn × Rn → R = (-∞, + ∞) that is additively homogeneous in one (or both) of the variables we also compare the first conjugates associated to the same coupling. We give an application to the "min-type" coupling function arising in the study of topical functions.
Original languageEnglish
Pages (from-to)285-297
JournalJournal of Convex Analysis
Volume15
Issue number2
Publication statusPublished - 2 Jul 2008

Keywords

  • Generalized conjugation
  • Hull operators
  • Topical functions

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