Liero, M. and Mielke, A. and Savaré, G. (2017) Optimal EntropyTransport problems and a new HellingerKantorovich distance between positive measures. Invent. math. . pp. 1149. ISSN 14321297 (online)

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Official URL: http://dx.doi.org/10.1007/s0022201707598
Abstract
We develop a full theory for the new class of Optimal EntropyTransport 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 EntropyTransport problems and introduce the new HellingerKantorovich 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 wellknown HellingerKakutani and KantorovichWasserstein distances.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint 08/2015 in arXiv:1508.07941 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
ID Code:  2179 
Deposited By:  Silvia Hoemke 
Deposited On:  16 Jan 2018 11:43 
Last Modified:  16 Jan 2018 11:43 
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