“FISTA” in Banach spaces with adaptive discretisations
Antonin Chambolle () and
Robert Tovey ()
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Antonin Chambolle: CNRS & Université Paris Dauphine, PSL Research University
Robert Tovey: INRIA Paris
Computational Optimization and Applications, 2022, vol. 83, issue 3, No 5, 845-892
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.
Keywords: Convex optimization; Multiscale; Multigrid; Sparsity; Lasso (search for similar items in EconPapers)
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