CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: An additive subfamily of enlargements of a maximally monotone operator Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 10:00 am, Wed, 15th Oct 2014 Abstract: We introduce a subfamily of enlargements of a maximally monotone operator $T$. Our definition is inspired by a 1988 publication of Fitzpatrick. These enlargements are elements of the family of enlargements $\mathbb{E}(T)$ introduced by Svaiter in 2000. These new enlargements share with the $\epsilon$-subdifferential a special additivity property, and hence they can be seen as structurally closer to the $\epsilon$-subdifferential. For the case $T=\nabla f$, we prove that some members of the subfamily are smaller than the $\epsilon$-subdifferential enlargement. In this case, we construct a specific enlargement which coincides with the $\epsilon$-subdifferential. Joint work with Juan Enrique Martínez Legaz, Mahboubeh Rezaei, and Michel Théra. [Permanent link]