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Representer theorems and convex optimization

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ASCW03 - Approximation, sampling, and compression in high dimensional problems

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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