Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric
Tahraoui, Rabah; Vialard, François-Xavier (2016), Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric. https://basepub.dauphine.fr/handle/123456789/17200
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01331110
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
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Abstract (EN)We study a second-order variational problem on the group of diffeomorphisms of the interval [0, 1] endowed with a right-invariant Sobolev metric of order 2, which consists in the minimization of the acceleration. We compute the relaxation of the problem which involves the so-called Fisher-Rao functional a convex functional on the space of measures. This relaxation enables the derivation of several optimality conditions and, in particular, a sufficient condition which guarantees that a given path of the initial problem is also a minimizer of the relaxed one. This sufficient condition is related to the existence of a solution to a Riccati equation involving the path acceleration.
Subjects / KeywordsRight-invariant metric; Group of Diffeomorphisms; Fisher-Rao; Riemannian splines
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Benamou, Jean-David; Gallouët, Thomas; Vialard, François-Xavier (2019) Article accepté pour publication ou publié