"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/123456789/22783
TypeDocument de travail / Working paper
External document linkhttps://hal.inria.fr/hal-03119773
Series titleCahier de recherche CEREMADE, Université Paris Dauphine-PSL
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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.
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