
"FISTA" in Banach spaces with adaptive discretisations
Chambolle, Antonin; Tovey, R. (2021), "FISTA" in Banach spaces with adaptive discretisations. https://basepub.dauphine.psl.eu/handle/123456789/22272
View/ Open
Type
Document de travail / Working paperExternal document link
https://hal.inria.fr/hal-03119773Date
2021Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSLPublished in
Paris
Pages
36
Metadata
Show full item recordAbstract (EN)
FISTA is a popular convex optimisation algorithm which is known to converge at an optimal rate whenever the optimisation domain is contained in a suitable Hilbert space. We propose a modified algorithm where each iteration is performed in a subspace, and that subspace is allowed to change at every iteration. Analytically, this allows us to guarantee convergence in a Banach space setting, although at a reduced rate depending on the conditioning of the specific problem. Numerically we show that a greedy adaptive choice of discretisation can greatly increase the time and memory efficiency in infinite dimensional Lasso optimisation problems.Related items
Showing items related by title and author.
-
Chambolle, Antonin; Tovey, R. (2021) Document de travail / Working paper
-
Vigeral, Guillaume (2010) Article accepté pour publication ou publié
-
Chambolle, Antonin; Dal Maso, Gianni (1999) Article accepté pour publication ou publié
-
Alouges, François; Chambolle, Antonin; Stantejsky, Dominik (2021) Article accepté pour publication ou publié
-
Chambolle, Antonin (1995) Article accepté pour publication ou publié