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"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 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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Preprints, Working Papers, ...
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Contributor : Robert Tovey Connect in order to contact the contributor
Submitted on : Monday, January 25, 2021 - 9:53:05 AM
Last modification on : Friday, January 21, 2022 - 3:09:48 AM

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  • HAL Id : hal-03119773, version 1
  • ARXIV : 2101.09175



Antonin Chambolle, Robert Tovey. "FISTA" in Banach spaces with adaptive discretisations. 2021. ⟨hal-03119773⟩



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