{"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/proportional-integral-projected-gradient-1","title":"Proportional-Integral Projected Gradient Method for Conic Optimization","arxiv_id":"2108.10260","date":"2021-08-23","proceeding":null,"authors":["Yue Yu","Purnanand Elango","Ufuk Topcu","Behçet Açıkmeşe"],"abstract":"Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient method (PIPG). PIPG ensures that both the primal-dual gap and the constraint violation converge to zero at the rate of \\(O(1/k)\\), where \\(k\\) is the number of iterations. If the objective function is strongly convex, PIPG improves the convergence rate of the primal-dual gap to \\(O(1/k^2)\\). Further, unlike any existing first-order methods, PIPG also improves the convergence rate of the constraint violation to \\(O(1/k^3)\\). We demonstrate the application of PIPG in constrained optimal control problems.","url_abs":"https://arxiv.org/abs/2108.10260v2","url_pdf":"https://arxiv.org/pdf/2108.10260v2.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":"proportional-integral-projected-gradient-1","repo_url":"https://github.com/purnanandelango/pipg-demo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"proportional-integral-projected-gradient-1","repo_url":"https://github.com/uw-acl/pipg-demo","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}