Linear convergence of stochastic block-coordinate fixed point algorithms

Patrick L Combettes (1) , Jean-Christophe Pesquet (2, 3)

1 NC State - North Carolina State University [Raleigh]
2 CVN - Centre de vision numérique
3 GALEN-POST - Organ Modeling through Extraction, Representation and Understanding of Medical Image Content

Recent random block-coordinate fixed point algorithms are particularly well suited to large-scale optimization in signal and image processing. These algorithms feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. The present paper provides new linear convergence results. These convergence rates are compared to those of standard deter-ministic algorithms both theoretically and experimentally in an image recovery problem.

Mots clés: Block-coordinate algorithm; linear convergence; fixed-point algorithm; stochastic algorithm

Domaines: Automatique / Robotique; Optimisation et contrôle [math.OC]

Patrick L Combettes, Jean-Christophe Pesquet. Linear convergence of stochastic block-coordinate fixed point algorithms. European Signal and Image Processing Conference (EUSIPCO 2018), Sep 2018, Rome, Italy. ⟨10.23919/EUSIPCO.2018.8552941⟩. ⟨hal-01964580⟩