{"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/a-unified-optimization-framework-for-low-rank-1","title":"A Unified Optimization Framework for Low-Rank Inducing Penalties","arxiv_id":"2001.08415","date":"2020-01-23","proceeding":null,"authors":["Marcus Valtonen Örnhag","Carl Olsson","Anders Heyden"],"abstract":"In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens up for possibilities of combining the best of both worlds, and to leverage each methods contribution to cases where simply enforcing one of the regularizers are insufficient. We show that the proposed regularizers can be incorporated in standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), and other subgradient methods. Furthermore, we provide an efficient way of computing the proximal operator. Lastly, we show on real non-rigid structure-from-motion (NRSfM) datasets, the issues that arise from using weighted nuclear norm penalties, and how this can be remedied using our proposed method.","url_abs":"https://arxiv.org/abs/2001.08415v1","url_pdf":"https://arxiv.org/pdf/2001.08415v1.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":"a-unified-optimization-framework-for-low-rank-1","repo_url":"https://github.com/marcusvaltonen/UnifiedFramework","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}