{"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/nonsmooth-convex-optimization-using-the","title":"Nonsmooth Convex Optimization using the Specular Gradient Method with Root-Linear Convergence","arxiv_id":"2412.20747","date":"2024-12-30","proceeding":null,"authors":["Kiyuob Jung","Jehan Oh"],"abstract":"We propose the specular gradient method for one-dimensional convex optimization. Assuming that the minimum is attained and a suitable initial distance bound holds, we establish R-linear convergence using normalized steps of geometrically decreasing length. Neither strong convexity nor differentiability is required.","url_abs":"https://arxiv.org/abs/2412.20747v1","url_pdf":"https://arxiv.org/pdf/2412.20747v1.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":"nonsmooth-convex-optimization-using-the","repo_url":"https://github.com/kyjung2357/sgm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}