- Title
- An additive subfamily of enlargements of a maximally monotone operator
- Creator
- Burachik, Regina; Martinez-Legaz, Juan; Rezaie, Mahboubeh; Thera, Michel
- Date
- 2015
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100313
- Identifier
- vital:10516
- Identifier
-
https://doi.org/10.1007/s11228-015-0340-9
- Identifier
- ISSN:1877-0533
- Abstract
- 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 epsilon-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the epsilon-subdifferential enlargement.
- Publisher
- Springer Netherlands
- Relation
- Set-Valued and Variational Analysis Vol. 23, no. 4 (2015), p. 643-665
- Rights
- Copyright © Springer Science+Business Media Dordrecht 2015
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; Maximally monotone operator; ε-subdifferential mapping; Subdifferential operator; Convex lower semicontinuous function; Fitzpatrick function; Enlargement of an operator; Brøndsted- Rockafellar enlargements; Additive enlargements; Fenchel-Young function
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