{"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-search-free-o-1-k-3-2-homotopy-inexact","title":"A search-free $O(1/k^{3/2})$ homotopy inexact proximal-Newton extragradient algorithm for monotone variational inequalities","arxiv_id":"2308.05887","date":"2023-08-11","proceeding":null,"authors":["M. Marques Alves","João M. Pereira","Benar F. Svaiter"],"abstract":"We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from Monteiro and Svaiter (2012) by introducing a novel approach based on homotopy, which requires the resolution (at each iteration) of a single strongly monotone linear variational inequality. For a given tolerance $\\rho>0$, our main algorithm exhibits pointwise $O\\left(\\frac{1}{\\rho}\\right)$ and ergodic $O\\left(\\frac{1}{\\rho^{2/3}}\\right)$ iteration-complexities. From a practical perspective, preliminary numerical experiments indicate that our main algorithm outperforms some previous proximal-Newton schemes.","url_abs":"https://arxiv.org/abs/2308.05887v2","url_pdf":"https://arxiv.org/pdf/2308.05887v2.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-search-free-o-1-k-3-2-homotopy-inexact","repo_url":"https://github.com/joaompereira/hipnex","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2308.05887","atlas_url":"https://app.syntology.ai/?focus=2308.05887","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}