{"paper":{"title":"Dual potentials for capacity constrained optimal transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christian Seis, Jonathan Korman, Robert J. McCann","submitted_at":"2013-07-30T01:39:01Z","abstract_excerpt":"Optimal transportation with capacity constraints, a variant of the well-known optimal transportation problem, is concerned with transporting one probability density $f \\in L^1(\\mathbb{R}^m)$ onto another one $g \\in L^1(\\mathbb{R}^n)$ so as to optimize a cost function $c \\in L^1(\\mathbb{R}^{m+n})$ while respecting the capacity constraints $0\\le h \\le \\bar h\\in L^\\infty(\\mathbb{R}^{m+n})$.\n  A linear programming duality theorem for this problem was first established by Levin. In this note, we prove under mild assumptions on the given data, the existence of a pair of $L^1$-functions optimizing th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7774","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}