{"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/block-factor-width-two-matrices-in","title":"Block Factor-Width-Two Matrices in Semidefinite Programming","arxiv_id":"1903.04938","date":"2019-03-12","proceeding":null,"authors":["Aivar Sootla","Yang Zheng","Antonis Papachristodoulou"],"abstract":"In this paper, we introduce a set of block factor-width-two matrices, which is a generalisation of factor-width-two matrices and is a subset of positive semidefinite matrices. The set of block factor-width-two matrices is a proper cone and we compute a closed-form expression for its dual cone. We use these cones to build hierarchies of inner and outer approximations of the cone of positive semidefinite matrices. The main feature of these cones is that they enable a decomposition of a large semidefinite constraint into a number of smaller semidefinite constraints. As the main application of these classes of matrices, we envision large-scale semidefinite feasibility optimisation programs including sum-of-squares (SOS) programs. We present numerical examples from SOS optimisation showcasing the properties of this decomposition.","url_abs":"http://arxiv.org/abs/1903.04938v1","url_pdf":"http://arxiv.org/pdf/1903.04938v1.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":"block-factor-width-two-matrices-in","repo_url":"https://github.com/zhengy09/SDPfw","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"block-factor-width-two-matrices-in","repo_url":"https://github.com/soc-ucsd/sdpfw","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}