{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/computing-the-proximal-operator-of-the-ell-1","title":"Computing the proximal operator of the $\\ell_1$ induced matrix norm","arxiv_id":"2005.06804","date":"2020-05-14","proceeding":null,"authors":["Jeremy E. Cohen"],"abstract":"In this short article, for any matrix $X\\in\\mathbb{R}^{n\\times m}$ the proximity operator of two induced norms $ \\|X\\|_1 $ and $ \\|X\\|_{\\infty}$ are derived. Although no close form expression is obtained, an algorithmic procedure is described which costs roughly $\\mathcal{O}(nm)$. This algorithm relies on a bisection on a real parameter derived from the Karush-Kuhn-Tucker conditions, following the proof idea of the proximal operator of the $ \\max $ function found in Parikh(2014).","url_abs":"http://arxiv.org/abs/2005.06804v2","url_pdf":"http://arxiv.org/pdf/2005.06804v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"computing-the-proximal-operator-of-the-ell-1","repo_url":"https://github.com/cohenjer/Tensor_codes/tree/master/Dictionary-based_decomposition/ProxOp","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}