Representer theorems and convex optimization
Duration: 44 mins 8 secs
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About this item
| Description: |
Boyer, C
Monday 17th June 2019 - 15:40 to 16:30 |
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| Created: | 2019-06-18 09:23 |
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| Collection: | Approximation, sampling, and compression in high dimensional problems |
| Publisher: | Isaac Newton Institute |
| Copyright: | Boyer, C |
| Language: | eng (English) |
| 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. 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. |
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