{"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/variational-principles-for-minkowski-type","title":"Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations","arxiv_id":"1302.5472","date":"2013-02-22","proceeding":null,"authors":["Xianfeng Gu","Feng Luo","Jian Sun","S. -T. Yau"],"abstract":"In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computational geometry is established.","url_abs":"http://arxiv.org/abs/1302.5472v1","url_pdf":"http://arxiv.org/pdf/1302.5472v1.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":"variational-principles-for-minkowski-type","repo_url":"https://github.com/icemiliang/pyvot","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1302.5472","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}