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A mixed finite element discretization of dynamical optimal transport

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MixedFiniteElementsHAL.pdf (1.117Mb)
Date
2020
Publisher city
Paris
Collection title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Link to item file
https://hal.archives-ouvertes.fr/hal-02501634
Dewey
Analyse
Sujet
dynamical optimal transport
URI
https://basepub.dauphine.fr/handle/123456789/20681
Collections
  • CEREMADE : Publications
Metadata
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Author
Natale, Andrea
1042458 Laboratoire de Mathématiques d'Orsay [LMO]
Todeschi, Gabriele
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
25
Abstract (EN)
In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the finite element setting the finite difference scheme proposed by Papadakis et al. [SIAM J Imaging Sci, 7(1):212–238,2014]. We solve the discrete problem using a proximal-splitting approach and we show how to modify this in the presence of regularization terms which are relevant for imaging applications.

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