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Journal Articles Computational Optimization and Applications Year : 2022

"FISTA" in Banach spaces with adaptive discretisations

Abstract

FISTA is a popular convex optimisation algorithm which is known to converge at an optimal rate whenever a minimiser is contained in a suitable Hilbert space. We propose a modified algorithm where each iteration is performed in a subset which is allowed to change at every iteration. Sufficient conditions are provided for guaranteed convergence, although at a reduced rate depending on the conditioning of the specific problem. These conditions have a natural interpretation when a minimiser exists in an underlying Banach space. Typical examples are L1-penalised reconstructions where we provide detailed theoretical and numerical analysis.
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hal-03119773 , version 1 (05-10-2022)

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Antonin Chambolle, Robert Tovey. "FISTA" in Banach spaces with adaptive discretisations. Computational Optimization and Applications, 2022, 83 (3), pp.845--892. ⟨10.1007/s10589-022-00418-3⟩. ⟨hal-03119773⟩
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