{"ID":2865452,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.22494","arxiv_id":"2509.22494","title":"A dynamical formulation of multi-marginal optimal transport","abstract":"We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical dynamical approach of Benamou-Brenier. Our dynamical formulation yields a convex optimization problem, enabling the use of convex optimization tools to find quasi-Monge solutions of the static multi-marginal problem for translation-invariant costs. We illustrate our results numerically with proximal splitting methods.","short_abstract":"We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical dynamical approach of Benamou-Brenier. Our dynamical formulation yields a convex opti...","url_abs":"https://arxiv.org/abs/2509.22494","url_pdf":"https://arxiv.org/pdf/2509.22494v2","authors":"[\"Brendan Pass\",\"Yair Shenfeld\"]","published":"2025-09-26T15:37:51Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.AP\",\"math.PR\"]","methods":"[]","has_code":false}