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“FISTA” in Banach spaces with adaptive discretisations

Author

Listed:
  • Antonin Chambolle

    (CNRS & Université Paris Dauphine, PSL Research University)

  • Robert Tovey

    (INRIA Paris)

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.

Suggested Citation

  • Antonin Chambolle & Robert Tovey, 2022. "“FISTA” in Banach spaces with adaptive discretisations," Computational Optimization and Applications, Springer, vol. 83(3), pages 845-892, December.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:3:d:10.1007_s10589-022-00418-3
    DOI: 10.1007/s10589-022-00418-3
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