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On Representer Theorems and Convex Regularization
June 26, 2018 Β· Declared Dead Β· π SIAM Journal on Optimization
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Authors
Claire Boyer, Antonin Chambolle, Yohann De Castro, Vincent Duval, FrΓ©dΓ©ric De Gournay, Pierre Weiss
arXiv ID
1806.09810
Category
math.OC: Optimization & Control
Cross-listed
cs.IT
Citations
118
Venue
SIAM Journal on Optimization
Last Checked
4 months ago
Abstract
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. An extension to a broader class of quasi-convex regularizers is also discussed. As a side result, we characterize the minimizers of the total gradient variation, which was still an unresolved problem.
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