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Journal of Convex Analysis 28 (2021), No. 3, [final page numbers not yet available]
Copyright Heldermann Verlag 2021

An Epigraphical Approach to the Representer Theorem

Vincent Duval
INRIA and CEREMADE, Université Paris-Dauphine, Paris, France

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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