Representer theorems and convex optimization – Claire Boyer (Sorbonne Université; ENS – Paris)

June 17, 2019 @ 3:40 pm – 4:30 pm
Seminar Room 1
Newton Institute

We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and elements of the extreme rays of the regularizer level sets. As a side result, we characterize the minimizers of the total gradient variation. As an ongoing work, we will also study the geometry of the total gradient variation ball. This is a joint work with Antonin Chambolle, Yohann De Castro, Vincent Duval, Frédéric de Gournay, and Pierre Weiss.