Stability of over-relaxations for the Forward-Backward algorithm, application to FISTA

Abstract : 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.
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Submitted on : Friday, June 12, 2015 - 6:59:31 PM
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Jean-François Aujol, Charles Dossal. Stability of over-relaxations for the Forward-Backward algorithm, application to FISTA. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2015. ⟨hal-01163432⟩

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