{"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/exploiting-term-sparsity-in-noncommutative","title":"Exploiting term sparsity in Noncommutative Polynomial Optimization","arxiv_id":"2010.06956","date":"2020-10-14","proceeding":null,"authors":["Jie Wang","Victor Magron"],"abstract":"We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS, to solve large-scale sparse noncommutative polynomial optimization problems. This hierarchy features the exploitation of term sparsity hidden in the input data for eigenvalue and trace optimization problems. NCTSSOS complements the recent work that exploits correlative sparsity for noncommutative optimization problems by Klep, Magron and Povh in arXiv:1909.00569, and is the noncommutative analogue of the TSSOS framework by Wang, Magron and Lasserre in arXiv:1912.08899. We also propose an extension exploiting simultaneously correlative and term sparsity, as done previously in the commutative case arXiv:2005.02828. Under certain conditions, we prove that the optimums of the NCTSSOS hierarchy converge to the optimum of the corresponding dense SDP relaxation. We illustrate the efficiency and scalability of NCTSSOS by solving eigenvalue/trace optimization problems from the literature as well as randomly generated examples involving up to several thousands of variables.","url_abs":"http://arxiv.org/abs/2010.06956v1","url_pdf":"http://arxiv.org/pdf/2010.06956v1.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":"exploiting-term-sparsity-in-noncommutative","repo_url":"https://github.com/wangjie212/NCTSSOS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2010.06956","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}