{"ID":2877002,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.20428","arxiv_id":"2508.20428","title":"A note on the c-monotonicity in optimal transport with capacity constraints","abstract":"This paper studies the geometry of the optimizer for the optimal transport problem with capacity constraints. We introduce the concept of c-capacity monotonicity, which is a generalization of c-cyclical monotonicity in optimal transport. We show that the optimizer of the optimal transport problem with capacity constraints is c-capacity monotone.","short_abstract":"This paper studies the geometry of the optimizer for the optimal transport problem with capacity constraints. We introduce the concept of c-capacity monotonicity, which is a generalization of c-cyclical monotonicity in optimal transport. We show that the optimizer of the optimal transport problem with capacity constrai...","url_abs":"https://arxiv.org/abs/2508.20428","url_pdf":"https://arxiv.org/pdf/2508.20428v2","authors":"[\"Dongwei Chen\"]","published":"2025-08-28T04:57:02Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}