{"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/proximal-quasi-newton-method-for-composite","title":"Proximal Quasi-Newton Method for Composite Optimization over the Stiefel Manifold","arxiv_id":"2501.09516","date":"2025-01-16","proceeding":null,"authors":["Qinsi Wang","Wei Hong Yang"],"abstract":"In this paper, we consider the composite optimization problems over the Stiefel manifold. A successful method to solve this class of problems is the proximal gradient method proposed by Chen et al. Motivated by the proximal Newton-type techniques in the Euclidean space, we present a Riemannian proximal quasi-Newton method, named ManPQN, to solve the composite optimization problems. The global convergence of the ManPQN method is proved and iteration complexity for obtaining an $\\epsilon$-stationary point is analyzed. Under some mild conditions, we also establish the local linear convergence result of the ManPQN method. Numerical results are encouraging, which shows that the proximal quasi-Newton technique can be used to accelerate the proximal gradient method.","url_abs":"https://arxiv.org/abs/2501.09516v1","url_pdf":"https://arxiv.org/pdf/2501.09516v1.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":"proximal-quasi-newton-method-for-composite","repo_url":"https://github.com/QinsiWang2022/ManPQN","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}