An additive subfamily of enlargements of a maximally monotone operator
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 subdiffer...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:184720 |
| Acceso en línea: | https://ddd.uab.cat/record/184720 https://dx.doi.org/urn:doi:10.1007/s11228-015-0340-9 |
| Access Level: | acceso abierto |
| Palabra clave: | Maximally monotone operator ε-subdifferential mapping Subdifferential operator Convex lower semicontinuous function Fitzpatrick function Enlargement of an operator Brøndsted- Rockafellar enlargements Additive enlargements Brøndsted- Rockafellar property Fenchel-Young function |
| Sumario: | 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. |
|---|