{"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-generalized-newton-method-for-subgradient","title":"A Generalized Newton Method for Subgradient Systems","arxiv_id":"2009.10551","date":"2020-09-22","proceeding":null,"authors":["Pham Duy Khanh","Boris Mordukhovich","Vo Thanh Phat"],"abstract":"This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order subdifferential of such functions that enjoys extensive calculus rules and can be efficiently computed for broad classes of extended-real-valued functions. Based on this and on metric regularity and subregularity properties of subgradient mappings, we establish verifiable conditions ensuring well-posedness of the proposed algorithm and its local superlinear convergence. The obtained results are also new for the class of equations defined by continuously differentiable functions with Lipschitzian gradients (${\\cal C}^{1,1}$ functions), which is the underlying case of our consideration. The developed algorithms for prox-regular functions and its extension to a structured class of composite functions are formulated in terms of proximal mappings and forward-backward envelopes. Besides numerous illustrative examples and comparison with known algorithms for ${\\cal C}^{1,1}$ functions and generalized equations, the paper presents applications of the proposed algorithms to regularized least square problems arising in statistics, machine learning, and related disciplines.","url_abs":"https://arxiv.org/abs/2009.10551v2","url_pdf":"https://arxiv.org/pdf/2009.10551v2.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-generalized-newton-method-for-subgradient","repo_url":"https://github.com/he9180/GDNM","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}