{"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/piecewise-polyhedral-formulations-for-a","title":"Piecewise Polyhedral Formulations for a Multilinear Term","arxiv_id":"2001.00514","date":"2020-01-02","proceeding":null,"authors":["Kaarthik Sundar","Harsha Nagarajan","Jeff Linderoth","Site Wang","Russell Bent"],"abstract":"In this paper, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex hull representation. Based on the solution of the PPR, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on instances of standard benchmarks of nonlinear programs (NLPs) with multilinear terms and compare the proposed formulation with a traditional formulation that is built by recursively relaxing bilinear groupings of multilinear terms.","url_abs":"https://arxiv.org/abs/2001.00514v3","url_pdf":"https://arxiv.org/pdf/2001.00514v3.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":"piecewise-polyhedral-formulations-for-a","repo_url":"https://github.com/sujeevraja/PolyhedralRelaxations.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}