{"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-first-order-primal-dual-algorithm-with","title":"A first-order primal-dual algorithm with linesearch","arxiv_id":"1608.08883","date":"2016-08-31","proceeding":null,"authors":["Yura Malitsky","Thomas Pock"],"abstract":"The paper proposes a linesearch for a primal-dual method. Each iteration of the linesearch requires to update only the dual (or primal) variable. For many problems, in particular for regularized least squares, the linesearch does not require any additional matrix-vector multiplications. We prove convergence of the proposed method under standard assumptions. We also show an ergodic $O(1/N)$ rate of convergence for our method. In case one or both of the prox-functions are strongly convex, we modify our basic method to get a better convergence rate. Finally, we propose a linesearch for a saddle point problem with an additional smooth term. Several numerical experiments confirm the efficiency of our proposed methods.","url_abs":"http://arxiv.org/abs/1608.08883v2","url_pdf":"http://arxiv.org/pdf/1608.08883v2.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-first-order-primal-dual-algorithm-with","repo_url":"https://github.com/ymalitsky/primal-dual-linesearch","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1608.08883","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}