{"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/local-convergence-of-proximal-splitting","title":"Local Convergence of Proximal Splitting Methods for Rank Constrained Problems","arxiv_id":"1710.04248","date":"2017-10-11","proceeding":null,"authors":["Christian Grussler","Pontus Giselsson"],"abstract":"We analyze the local convergence of proximal splitting algorithms to solve\noptimization problems that are convex besides a rank constraint. For this, we\nshow conditions under which the proximal operator of a function involving the\nrank constraint is locally identical to the proximal operator of its convex\nenvelope, hence implying local convergence. The conditions imply that the\nnon-convex algorithms locally converge to a solution whenever a convex\nrelaxation involving the convex envelope can be expected to solve the\nnon-convex problem.","url_abs":"http://arxiv.org/abs/1710.04248v1","url_pdf":"http://arxiv.org/pdf/1710.04248v1.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":"abstracts"},"code_links":[{"paper_slug":"local-convergence-of-proximal-splitting","repo_url":"https://github.com/LowRankOpt/LRINorm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"local-convergence-of-proximal-splitting","repo_url":"https://github.com/LowRankOpt/LRIPy","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}