{"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/performance-estimation-for-smooth-and","title":"Performance Estimation for Smooth and Strongly Convex Sets","arxiv_id":"2410.14811","date":"2024-10-18","proceeding":null,"authors":["Alan Luner","Benjamin Grimmer"],"abstract":"We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove ``interpolation theorems'' for smooth and strongly convex sets with interior point conditions and bounded diameter, showing a wide range of extremal questions amount to structured mathematical programs. Prior function interpolation theorems are recovered as a limit of our set interpolation theory. Our theory provides finite-dimensional formulations of performance estimation problems for algorithms utilizing separating hyperplane oracles and linear optimization oracles of smooth/strongly convex sets. As applications of this computer-assisted machinery, we identify a minimax optimal separating hyperplane method and areas for improvement in the theory of Frank-Wolfe and non-Lipschitz Smooth Optimization.","url_abs":"https://arxiv.org/abs/2410.14811v2","url_pdf":"https://arxiv.org/pdf/2410.14811v2.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":"performance-estimation-for-smooth-and","repo_url":"https://github.com/alanluner/pepstructuredsets","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":"https://app.syntology.ai/?focus=2410.14811","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}