Corpus ID: 182952597

Hidden Convexity in the l0 Pseudonorm

@article{Chancelier2020HiddenCI,
  title={Hidden Convexity in the l0 Pseudonorm},
  author={J. Chancelier and M. Lara},
  journal={arXiv: Optimization and Control},
  year={2020}
}
The so-called l0 pseudonorm counts the number of nonzero components of a vector of a Euclidian space. 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, E-Capra, that has the property of being constant along primal rays like the l0 pseudonorm. The coupling E-Capra belongs to the class of one-sided linear couplings, that we introduce; we show that they induce… Expand

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