On the total variation Wasserstein gradient flow and the TV-JKO scheme
Carlier, Guillaume; Poon, Clarice (2019), On the total variation Wasserstein gradient flow and the TV-JKO scheme, ESAIM. Control, Optimisation and Calculus of Variations, 25, p. 21. 10.1051/cocv/2018042
View/ Open
Type
Article accepté pour publication ou publiéDate
2019Journal name
ESAIM. Control, Optimisation and Calculus of VariationsVolume
25Publisher
EDP Sciences
Pages
21
Publication identifier
Metadata
Show full item recordAuthor(s)
Carlier, GuillaumeCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Poon, Clarice
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Applied Mathematics and Theoretical Physics [DAMTP]
Abstract (EN)
We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a sort of maximum principle and the regularity of level sets). We study in detail the case of step functions. Finally, in dimension one, we establish convergence as the time step goes to zero to a solution of a fourth-order nonlinear evolution equation.Subjects / Keywords
fourth-order evolution equations; JKO scheme; total variation; Wasserstein gradient flowsRelated items
Showing items related by title and author.
-
Chambolle, Antonin; Duval, Vincent; Peyré, Gabriel; Poon, Clarice (2016) Communication / Conférence
-
Chambolle, Antonin; Duval, Vincent; Peyré, Gabriel; Poon, Clarice (2016) Article accepté pour publication ou publié
-
Legendre, Guillaume; Turinici, Gabriel (2017) Article accepté pour publication ou publié
-
Benamou, Jean-David; Carlier, Guillaume; Laborde, Maxime (2016) Article accepté pour publication ou publié
-
Wasserstein gradient flow of the Fisher information from a non-smooth convex minimization viewpoint Carlier, Guillaume; Benamou, Jean-David; Matthes, Daniel (2023) Document de travail / Working paper