Abstract

We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with strongly convex regularization and general data-fit functions. We develop an inertial approach of which we analyze both convergence and stability properties. Using tools from inexact proximal calculus, we prove early stopping results with optimal convergence rates for additive data terms and further consider more general cases, such as the Kullback--Leibler divergence, for which different type of proximal point approximations hold.

Keywords

  1. iterative regularization
  2. duality
  3. acceleration
  4. forward-backward splitting
  5. diagonal methods
  6. stability and convergence analysis

MSC codes

  1. 90C25
  2. 49N45
  3. 49N15
  4. 68U10
  5. 90C06

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Information & Authors

Information

Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization
Pages: 754 - 784
ISSN (online): 1095-7189

History

Submitted: 27 December 2019
Accepted: 29 October 2020
Published online: 1 March 2021

Keywords

  1. iterative regularization
  2. duality
  3. acceleration
  4. forward-backward splitting
  5. diagonal methods
  6. stability and convergence analysis

MSC codes

  1. 90C25
  2. 49N45
  3. 49N15
  4. 68U10
  5. 90C06

Authors

Affiliations

Funding Information

Centre National de la Recherche Scientifique https://doi.org/10.13039/501100004794

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