{"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/efficient-proximal-mapping-computation-for","title":"Efficient Proximal Mapping Computation for Unitarily Invariant Low-Rank Inducing Norms","arxiv_id":"1810.07570","date":"2018-10-17","proceeding":null,"authors":["Christian Grussler","Pontus Giselsson"],"abstract":"Low-rank inducing unitarily invariant norms have been introduced to convexify\nproblems with low-rank/sparsity constraint. They are the convex envelope of a\nunitary invariant norm and the indicator function of an upper bounding rank\nconstraint. The most well-known member of this family is the so-called nuclear\nnorm. To solve optimization problems involving such norms with proximal\nsplitting methods, efficient ways of evaluating the proximal mapping of the\nlow-rank inducing norms are needed. This is known for the nuclear norm, but not\nfor most other members of the low-rank inducing family. This work supplies a\nframework that reduces the proximal mapping evaluation into a nested binary\nsearch, in which each iteration requires the solution of a much simpler\nproblem. This simpler problem can often be solved analytically as it is\ndemonstrated for the so-called low-rank inducing Frobenius and spectral norms.\nMoreover, the framework allows to compute the proximal mapping of compositions\nof these norms with increasing convex functions and the projections onto their\nepigraphs. This has the additional advantage that we can also deal with\ncompositions of increasing convex functions and low-rank inducing norms in\nproximal splitting methods.","url_abs":"http://arxiv.org/abs/1810.07570v1","url_pdf":"http://arxiv.org/pdf/1810.07570v1.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":"efficient-proximal-mapping-computation-for","repo_url":"https://github.com/LowRankOpt/LRINorm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"efficient-proximal-mapping-computation-for","repo_url":"https://github.com/LowRankOpt/LRIPy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}