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"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

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Type
Document de travail / Working paper
External document link
https://hal.inria.fr/hal-03119773
Date
2021
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
36
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Author(s)
Chambolle, Antonin
Tovey, R.
Abstract (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.