Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric
Optimization and Control
2018-01-15 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1801.04146,
title = {Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric},
author = {François-Xavier Vialard},
journal= {arXiv preprint arXiv:1801.04146},
year = {2018}
}