Liero, M. and Mielke, A. and Savaré, G.
(2018)
*Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures.*
Inventiones mathematicae, 211
.
pp. 969-1117.
ISSN 1432-1297 (online)

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Official URL: https://doi.org/10.1007/s00222-017-0759-8

## Abstract

We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal Transport problems: given a couple 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, that 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.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2179 |

Deposited By: | Silvia Hoemke |

Deposited On: | 16 Jan 2018 11:43 |

Last Modified: | 17 Jan 2022 17:21 |

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