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Article Dans Une Revue SIAM Journal on Optimization Année : 2015

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

Jean-François Aujol
Charles H Dossal
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Résumé

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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hal-01163432 , version 1 (12-06-2015)

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  • HAL Id : hal-01163432 , version 1

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Jean-François Aujol, Charles H Dossal. Stability of over-relaxations for the Forward-Backward algorithm, application to FISTA. SIAM Journal on Optimization, 2015. ⟨hal-01163432⟩

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