{"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-subspace-accelerated-split-bregman-method","title":"A subspace-accelerated split Bregman method for sparse data recovery with joint l1-type regularizers","arxiv_id":"1912.06805","date":"2019-12-14","proceeding":null,"authors":["Valentina De Simone","Daniela di Serafino","Marco Viola"],"abstract":"We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form $f(\\mathbf{u})+\\tau_1 \\|\\mathbf{u}\\|_1 + \\tau_2 \\|D\\,\\mathbf{u}\\|_1$, where $f$ is a smooth convex function and $D$ represents a linear operator, e.g. a finite difference operator, as in anisotropic Total Variation and fused-lasso regularizations. Problems of this type arise in a wide variety of applications, including portfolio optimization and learning of predictive models from functional Magnetic Resonance Imaging (fMRI) data, and source detection problems in electroencephalography. The use of $\\|D\\,\\mathbf{u}\\|_1$ is aimed at encouraging structured sparsity in the solution. The subspaces where the acceleration is performed are selected so that the restriction of the objective function is a smooth function in a neighborhood of the current iterate. Numerical experiments on multi-period portfolio selection problems using real datasets show the effectiveness of the proposed method.","url_abs":"https://arxiv.org/abs/1912.06805v2","url_pdf":"https://arxiv.org/pdf/1912.06805v2.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-subspace-accelerated-split-bregman-method","repo_url":"https://github.com/diserafi/SBSA_QP","is_official":0,"mentioned_in_paper":0,"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}