Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Capra-subdifferential of the l0 pseudonorm   The l0 pseudonorm counts the nonzero coordinates of a vector. It is often
used in optimization problems to enforce the sparsity of the solution. However,
this function is nonconvex and noncontinuous, and optimization problems
formulated with l0 in the objective function or in the constraints are hard to
solve in general. Recently, a new family of coupling functions - called Capra
(constant along primal rays) - has proved to induce relevant generalized
Fenchel-Moreau conjugacies to handle the l0 pseudonorm. In particular, under a
suitable choice of source norm on the Euclidean space used in the definition of
the Capra coupling - the function l0 is Capra-subdifferentiable, hence is
Capra-convex. In this article, we give explicit formulations for the Capra
subdifferential of l0, when the source norm is a lp norm with p larger that 1.
We illustrate our results with graphical visualizations of the Capra
subdifferential of l0 for the Euclidean source norm.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga