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1831. The Geometry of Sparsity-Inducing Balls
Invited abstract in session TC-42: Variational Analysis and Subdifferential techniques, stream Variational Analysis and Continuous Optimization.
Tuesday, 12:30-14:00Room: 98 (building: 306)
Authors (first author is the speaker)
| 1. | Michel DE LARA
|
| École des Ponts ParisTech | |
| 2. | Jean-Philippe Chancelier
|
| CERMICS Ecole des Ponts et Chaussées, Université Paris Est | |
| 3. | Lionel Pournin
|
| Université Paris 13, Villetaneuse, France | |
| 4. | Antoine Deza
|
| McMaster University, Hamilton, Ontario, Canada |
Abstract
Sparse optimization seeks an optimal solution among vectors with at most k nonzero coordinates.
This constraint is hard to handle, and a strategy to overcome that difficulty
amounts to adding a norm penalty term to the objective function. The most widely used penalty
is based on the l1-norm which is recognized as the archetype of sparsity-inducing norms.
In this talk, we present generalized k-support norms, generated from a given source norm,
and show how they contribute to induce sparsity via support identification.
In case the source norms are the l1- and the l2-norms, we analyze the faces and normal cones
of the unit balls for the associated k-support norms and their dual top-k norms.
Keywords
- Continuous Optimization
- Convex Optimization
Status: accepted
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