Maximal Monotone Inclusions and Fitzpatrick Functions

par Joydeep Dutta (Indian Institute of Technology, Kanpur (India))

vendredi 26 juin 2015, 11:00 → 12:00 Europe/Paris

XLIM Salle X.203

In this talk we study maximal monotone inclusions from the perspective of gap functions. We propose a very natural gap function for an arbitrary maximal monotone inclusion, and will demonstrate how naturally this gap function arises from the Fitzpatrick function which is a convex function used to represent maximal monotone operators. This allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. We also study the special cases of a variational inequality and of a generalized variational inequality problem. The associated notion of a scalar gap is also considered in some detail. Corresponding local and global error bounds are also developed for the maximal monotone inclusion.