An Additive Subfamily of Enlargements of a Maximally Monotone Operator

Regina S. Burachik, Juan Enrique Martínez-Legaz, Mahboubeh Rezaie, Michel Théra

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Abstract

© 2015, Springer Science+Business Media Dordrecht. We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical ε-subdifferential enlargement widely used in convex analysis. We also recover the ε-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the ε-subdifferential enlargement.
Original languageEnglish
Pages (from-to)643-665
JournalSet-Valued and Variational Analysis
Volume23
Issue number4
DOIs
Publication statusPublished - 1 Dec 2015

Keywords

  • Additive enlargements
  • Brøndsted- Rockafellar enlargements
  • Brøndsted- Rockafellar property
  • Convex lower semicontinuous function
  • Enlargement of an operator
  • Fenchel-Young function
  • Fitzpatrick function
  • Maximally monotone operator
  • Subdifferential operator
  • ε-subdifferential mapping

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  • Cite this

    Burachik, R. S., Martínez-Legaz, J. E., Rezaie, M., & Théra, M. (2015). An Additive Subfamily of Enlargements of a Maximally Monotone Operator. Set-Valued and Variational Analysis, 23(4), 643-665. https://doi.org/10.1007/s11228-015-0340-9