Capra-Convexity, Convex Factorization and Variational Formulations for the ℓ0 Pseudonorm

@article{Chancelier2020CapraConvexityCF,
  title={Capra-Convexity, Convex Factorization and Variational Formulations for the ℓ0 Pseudonorm},
  author={Jean-Philippe Chancelier and Michel De Lara},
  journal={Set-Valued and Variational Analysis},
  year={2020},
  volume={30},
  pages={597-619}
}
The so-called ℓ 0 pseudonorm, or cardinality function, counts the number of nonzero components of a vector. In this paper, we analyze the ℓ 0 pseudonorm by means of so-called Capra (constant along primal rays) conjugacies, for which the underlying source norm and its dual norm are both orthant-strictly monotonic (a notion that we formally introduce and that encompasses the ℓ p -norms, but for the extreme ones). We obtain three main results. First, we show that the ℓ 0 pseudonorm is equal to its… 

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