{"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/projection-onto-a-simplex","title":"Projection Onto A Simplex","arxiv_id":"1101.6081","date":"2011-01-31","proceeding":null,"authors":["Yunmei Chen","Xiaojing Ye"],"abstract":"This mini-paper presents a fast and simple algorithm to compute the projection onto the canonical simplex $\\triangle^n$. Utilizing the Moreau's identity, we show that the problem is essentially a univariate minimization and the objective function is strictly convex and continuously differentiable. Moreover, it is shown that there are at most n candidates which can be computed explicitly, and the minimizer is the only one that falls into the correct interval.","url_abs":"http://arxiv.org/abs/1101.6081v2","url_pdf":"http://arxiv.org/pdf/1101.6081v2.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":"projection-onto-a-simplex","repo_url":"https://github.com/colewyeth/desc","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"projection-onto-a-simplex","repo_url":"https://github.com/lanha/SupResPALM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1101.6081","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}