{"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/relaxations-for-binary-polynomial","title":"Relaxations for binary polynomial optimization via signed certificates","arxiv_id":"2405.13447","date":"2024-05-22","proceeding":null,"authors":["Liding Xu","Leo Liberti"],"abstract":"We consider the problem of minimizing a polynomial $f$ over the (binary) hypercube. We show that, for a specific set of polynomials, their binary non-negativity (i.e. on the hypercube) can be checked in polynomial time via minimum cut algorithms, from which we construct a linear programming representation for this set of polynomials. We categorize binary polynomials according to their signed support patterns and develop parameterized linear programming representations for binary non-negative polynomials. This allows the construction of signed certificates of binary non-negativity with adjustable signed support patterns and representation complexities; and we propose a method for minimizing $f$ by decomposing it as a sum of signed certificates. This method yields new hierarchies of linear programming relaxations for binary polynomial optimization. Moreover, since our decomposition depends only on the support of $f$, the new hierarchies are sparsity-preserving.","url_abs":"https://arxiv.org/abs/2405.13447v1","url_pdf":"https://arxiv.org/pdf/2405.13447v1.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":"relaxations-for-binary-polynomial","repo_url":"https://github.com/lidingxu/BPOrelaxations","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}