{"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/graph-and-distributed-extensions-of-the","title":"Graph and distributed extensions of the Douglas-Rachford method","arxiv_id":"2211.04782","date":"2022-11-09","proceeding":null,"authors":["Kristian Bredies","Enis Chenchene","Emanuele Naldi"],"abstract":"In this paper, we propose several graph-based extensions of the Douglas-Rachford splitting (DRS) method to solve monotone inclusion problems involving the sum of $N$ maximal monotone operators. Our construction is based on a two-layer architecture that we refer to as bilevel graphs, to which we associate a generalization of the DRS algorithm that presents the prescribed structure. The resulting schemes can be understood as unconditionally stable frugal resolvent splitting methods with a minimal lifting in the sense of Ryu [Math Program 182(1):233-273, 2020], as well as instances of the (degenerate) Preconditioned Proximal Point method, which provides robust convergence guarantees. We further describe how the graph-based extensions of the DRS method can be leveraged to design new fully distributed protocols. Applications to a congested optimal transport problem and to distributed Support Vector Machines show interesting connections with the underlying graph topology and highly competitive performances with state-of-the-art distributed optimization approaches.","url_abs":"https://arxiv.org/abs/2211.04782v1","url_pdf":"https://arxiv.org/pdf/2211.04782v1.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":"graph-and-distributed-extensions-of-the","repo_url":"https://github.com/trade-opt/graph-drs","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}