Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric

François-Xavier Vialard (1, 2, 3)

1 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
2 Université Paris Dauphine-PSL
3 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this note, we propose a variational framework in which the minimization of the acceleration on the group of diffeomorphisms endowed with a right-invariant metric is well-posed. It relies on constraining the acceleration to belong to a Sobolev space of higher-order than the order of the metric in order to gain compactness. It provides the theoretical guarantee of existence of minimizers which is compulsory for numerical simulations.

Mots clés: Diffeomorphism groups; Right-invariant metric; Riemannian splines

Domaines: Optimisation et contrôle [math.OC]

François-Xavier Vialard. Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric. Mathematics of Shapes and Applications, p. 1 - 14, 2019, ⟨10.1142/9789811200137_0001⟩. ⟨hal-01682108⟩