On uniqueness of an optimal solution to the Kantorovich problem with density constraints

2024/01/13 by Svetlana Popova, Popova, Svetlana
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2401.07067

openalex publication_date 2024/01/13 · openalex created_date 2024/01/18 · openalex updated_date 2026/07/28

Abstract

We study optimal transportation problems with constraints on densities of transport plans. We obtain a sharp condition for the uniqueness of an optimal solution to the Kantorovich problem with density constraints, namely that the Borel measurable cost function h(x, y) satisfies the following non-degeneracy condition: h(x, y) can not be expressed as a sum of functions u(x) + v(y) on a set of positive measure.

Related

• A characterization for solutions of the Monge-Kantorovich mass transport problem
• On the Uniqueness of Kantorovich Potentials
• On nonlinear Kantorovich problems for cost functions of a special form
• Multi-marginal Monge-Kantorovich transport problems: A characterization\n of solutions
• Optimal Transportation with Capacity Constraints