Stability of over-relaxations for the Forward-Backward algorithm, application to FISTA
Langue
en
Article de revue
Ce document a été publié dans
SIAM Journal on Optimization. 2015-06-12p. www
Society for Industrial and Applied Mathematics
Résumé en anglais
This paper is concerned with the convergence of over-relaxations of FB algorithm (in particular FISTA), in the case when proximal maps and/or gradients are computed with a possible error. We show that provided these errors ...Lire la suite >
This paper is concerned with the convergence of over-relaxations of FB algorithm (in particular FISTA), in the case when proximal maps and/or gradients are computed with a possible error. We show that provided these errors are small enough, then the algorithm still converges to a minimizer of the functional, and with a speed of convergence (in terms of values of the functional) that remains the same as in the noise free case. We also show that larger errors can be allowed, using a lower over-relaxation than FISTA. This still leads to the convergence of iterates, and with ergodic convergence speed faster than the classical FB algorithm and FISTA.< Réduire
Mots clés en anglais
Convex analysis
proximal operator
FISTA
FB
over-relaxation.
Origine
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