On the total variation Wasserstein gradient flow and the TV-JKO scheme
Analysis of PDEs
2018-07-09 v2 Optimization and Control
Abstract
We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a form of maximum principle and in some cases, a minimum principle as well). Finally, we establish a convergence result as the time step goes to zero to a solution of a fourth-order nonlinear evolution equation, under the additional assumption that the density remains bounded away from zero. This lower bound is shown in dimension one and in the radially symmetric case.
Keywords
Cite
@article{arxiv.1703.00243,
title = {On the total variation Wasserstein gradient flow and the TV-JKO scheme},
author = {Guillaume Carlier and Clarice Poon},
journal= {arXiv preprint arXiv:1703.00243},
year = {2018}
}