Capra-convexity, convex factorization and variational formulations for the \(\ell_0\) pseudonorm

DOI10.1007/s11228-021-00606-zzbMath1500.46056arXiv2002.01314OpenAlexW3200480579WikidataQ114223370 ScholiaQ114223370MaRDI QIDQ2670982

Jean-Philippe Chancelier, Michel De Lara

Publication date: 3 June 2022

Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.01314

zbMATH Keywords

sparse optimization\( \ell_0\) pseudonormFenchel-Moreau conjugacygeneralized \(k\)-support dual normorthant-strictly monotonic norm

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Normed linear spaces and Banach spaces; Banach lattices (46B99) Convex functions and convex programs in convex geometry (52A41) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Duality theory (optimization) (49N15)

Related Items (2)

The Capra-subdifferential of the ℓ ₀ pseudonorm ⋮ Unnamed Item

Cites Work

• Relationship between the optimal solutions of least squares regularized with \(\ell_{0}\)-norm and constrained by \(k\)-sparsity
• A variational approach of the rank function
• Characterizations of \(^*\)orthant-monotonic norms
• Invertibility of functional Galois connections
• Characterizations of certain classes of norms
• Inf-convolution, sous-additivite, convexite des fonctions numériques
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• Variational Analysis
• Hidden Convexity in the l0 Pseudonorm
• Some Results on Fields of Values of a Matrix
• Abstract convexity and global optimization
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