An additive subfamily of enlargements of a maximally monotone operator

Regina Burachik (1) , Juan Enrique Martínez-Legaz (2) , Mahboubeh Rezaie (3) , Michel Théra (4)

1 University of South Australia
2 UAB - Universitat Autònoma de Barcelona = Autonomous University of Barcelona = Universidad Autónoma de Barcelona
3 University of Isfahan
4 XLIM-MATHIS - Mathématiques & Sécurité de l'information

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.

Domaines: Optimisation et contrôle [math.OC]

Regina Burachik, Juan Enrique Martínez-Legaz, Mahboubeh Rezaie, Michel Théra. An additive subfamily of enlargements of a maximally monotone operator. Set-Valued and Variational Analysis, 2015, 23 (4), pp.643-665. ⟨10.1007/s11228-015-0340-9⟩. ⟨hal-01314663⟩