Corpus ID: 119649017

A Suitable Conjugacy for the l0 Pseudonorm

@article{Chancelier2019ASC,
  title={A Suitable Conjugacy for the l0 Pseudonorm},
  author={Jean-Philippe Chancelier and Michel De Lara and Ponts Paristech},
  journal={arXiv: Optimization and Control},
  year={2019}
}
The so-called l0 pseudonorm on R d counts the number of nonzero components of a vector. It is well-known that the l0 pseudonorm is not convex, as its Fenchel biconjugate is zero. In this paper, we introduce a suitable conjugacy, induced by a novel coupling, Caprac, having the property of being constant along primal rays, like the l0 pseudonorm. The Caprac coupling belongs to the class of one-sided linear couplings, that we introduce. We show that they induce conjugacies that share nice… Expand
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