Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01331110
Contributor : François-Xavier Vialard <>
Submitted on : Tuesday, September 6, 2016 - 9:59:44 PM
Last modification on : Tuesday, February 5, 2019 - 11:44:32 AM

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  • HAL Id : hal-01331110, version 3
  • ARXIV : 1606.04230

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Rabah Tahraoui, François-Xavier Vialard. Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric. 2016. ⟨hal-01331110v3⟩

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