Idioma:

Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures

Liero, Matthias ; Mielke, Alexander ; Savaré, Giuseppe

Inventiones mathematicae, 2018-03, Vol.211 (3), p.969-1117 [Periódico revisado por pares]

Texto completo disponível

Citações Citado por

Título:
Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures
Autor: Liero, Matthias ; Mielke, Alexander ; Savaré, Giuseppe
Assuntos: Mathematics ; Mathematics and Statistics
É parte de: Inventiones mathematicae, 2018-03, Vol.211 (3), p.969-1117
Descrição: We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. These problems arise quite naturally by relaxing the marginal constraints typical of Optimal Transport problems: given a pair of finite measures (with possibly different total mass), one looks for minimizers of the sum of a linear transport functional and two convex entropy functionals, which quantify in some way the deviation of the marginals of the transport plan from the assigned measures. As a powerful application of this theory, we study the particular case of Logarithmic Entropy-Transport problems and introduce the new Hellinger–Kantorovich distance between measures in metric spaces . The striking connection between these two seemingly far topics allows for a deep analysis of the geometric properties of the new geodesic distance, which lies somehow between the well-known Hellinger–Kakutani and Kantorovich–Wasserstein distances.
Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
Idioma: Inglês

Voltar para lista de resultados