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• W3200480579 abstract "The so-called ℓ0 pseudonorm, or cardinality function, counts the number of nonzero components of a vector. In this paper, we analyze the ℓ0 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 ℓp-norms, but for the extreme ones). We obtain three main results. First, we show that the ℓ0 pseudonorm is equal to its Capra-biconjugate, that is, is a Capra-convex function. Second, we deduce an unexpected consequence, that we call convex factorization: the ℓ0 pseudonorm coincides, on the unit sphere of the source norm, with a proper convex lower semicontinuous function. Third, we establish a variational formulation for the ℓ0 pseudonorm by means of generalized top-k dual norms and k-support dual norms (that we formally introduce)." @default.
• W3200480579 created "2021-09-27" @default.
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• W3200480579 date "2021-09-21" @default.
• W3200480579 modified "2023-09-27" @default.
• W3200480579 title "Capra-Convexity, Convex Factorization and Variational Formulations for the ℓ0 Pseudonorm" @default.
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• W3200480579 doi "https://doi.org/10.1007/s11228-021-00606-z" @default.
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