Journal of Convex Analysis 28 (2021), No. 3, 819--836
Copyright Heldermann Verlag 2021
An Epigraphical Approach to the Representer Theorem
Vincent Duval
INRIA and CEREMADE, Université Paris-Dauphine, Paris, France
vincent.duval@inria.fr
Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems involving a finite number of measurements. We discuss its optimality on various problems concerning the recovery of Radon measures.
Keywords: Representer theorem, convex optimization, Carathéodory theorem.
MSC: 52A41, 90C25, 90C49.
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