Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators

Yboon García (1) , Marc Lassonde (2)

1 IMCA - Instituto de Matematica y Ciencias Afines
2 LAMIA - Laboratoire de Mathématiques Informatique et Applications

We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone operators.

Domaines: Optimisation et contrôle [math.OC]

Yboon García, Marc Lassonde. Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators. Set-Valued Analysis, 2012, 20 (1), pp.61-73. ⟨hal-00698802⟩