An additive subfamily of enlargements of a maximally monotone operator
Burachik, Regina (University of South Australia. School of Information Technology and Mathematical Sciences)
Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)
Rezaie, M. (University of Isfahan)
Théra, M. (Université de Limoges. Laboratoire XLIM)

Data:	2015
Resum:	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.
Ajuts:	Ministerio de Economía y Competitividad MTM2011-29064-C03
Nota:	Dedicated to professor L. Thibault
Nota:	Altres ajuts: Australian Research Council DP140103213 i DP110102011
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Llengua:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Matèria:	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
Publicat a:	Set-Valued and Variational Analysis, Vol. 23, Núm. 4 (December 2015) , p. 643-665 2015, ISSN 1877-0541

DOI: 10.1007/s11228-015-0340-9

Preprint 24 p, 473.9 KB

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