{"ID":2856751,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.10557","arxiv_id":"2510.10557","title":"Optimal transport paths with capacity induced cost function","abstract":"This article generalizes the study of ramified optimal transport with capacity constraint in transport multi-paths by generalizing the $\\mathbf{M}_α$ cost to $\\mathbf{M}_{α,c}$, which incorporates capacity constraints into the cost function. Equipped with $\\mathbf{M}_{α,c}$ cost, we prove the existence of optimal transport path, $\\mathbf{M}_{α,c}$ related inequalities, decomposition of any general transport paths, and occurrence of direct line segments in an optimal transport path.","short_abstract":"This article generalizes the study of ramified optimal transport with capacity constraint in transport multi-paths by generalizing the $\\mathbf{M}_α$ cost to $\\mathbf{M}_{α,c}$, which incorporates capacity constraints into the cost function. Equipped with $\\mathbf{M}_{α,c}$ cost, we prove the existence of optimal trans...","url_abs":"https://arxiv.org/abs/2510.10557","url_pdf":"https://arxiv.org/pdf/2510.10557v1","authors":"[\"Qinglan Xia\",\"Haotian Sun\"]","published":"2025-10-12T11:47:29Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}