87. The Geometry of Sparsity-Inducing Balls
Invited abstract in session FD-3: Variational techniques in optimization, stream Variational analysis: theory and algorithms.
Friday, 14:10 - 15:50Room: M:J
Authors (first author is the speaker)
| 1. | Michel De Lara
|
| École des Ponts ParisTech |
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
- Convex and non-smooth optimization
Status: accepted
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