2025/09/08 by Franc, Adrien Le, Chancelier, Jean-Philippe, de Lara, Michel +2
Computer Science · #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.2509.06392
This paper focuses on a specific form of abstract convexity known as Capra-convexity, where a constant along primal rays (Capra) coupling replaces the scalar product used in standard convex analysis to define generalized Fenchel conjugacies. A key motivating result is that the ℓ0 pseudonorm - which counts the number of nonzero components in a vector - is equal to its Capra-biconjugate. This implies that ℓ0 is a Capra-convex function, highlighting potential applications in statistics and machine learning, particularly for enforcing sparsity in models. Building on prior work characterizing the Capra-subdifferential of ℓ0 and the role of source norms in defining the Capra-coupling, the paper provides a characterization of Capra-convex sets.