Representative functions of maximally monotone operators and bifunctions

Monica Bianchi, Nicolas Hadjisavvas, Rita Pini

Research output: Contribution to journalArticlepeer-review

Abstract

The aim of this paper is to show that every representative function of a maximally monotone operator is the Fitzpatrick transform of a bifunction corresponding to the operator. In fact, for each representative function ϕ of the operator, there is a family of equivalent saddle functions (i.e., bifunctions which are concave in the first and convex in the second argument) each of which has ϕ as Fitzpatrick transform. In the special case where ϕ is the Fitzpatrick function of the operator, the family of equivalent saddle functions is explicitly constructed. In thiswaywe exhibit the relation between the recent theory of representative functions, and the much older theory of saddle functions initiated by Rockafellar.
Original languageEnglish
Pages (from-to)433-448
Number of pages16
JournalMathematical Programming
Volume2018
DOIs
Publication statusPublished - 2016

Keywords

  • Fitzpatrick function
  • Fitzpatrick transform
  • Maximal monotonicity
  • representative function

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