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Pré-Publication, Document De Travail Année : 2021

FISTA is an automatic geometrically optimized algorithm for strongly convex functions

Résumé

In this work, we are interested in the famous FISTA algorithm. We show that FISTA is an automatic geometrically optimized algorithm for functions satisfying a quadratic growth assumption. This explains why FISTA works better than the standard Forward-Backward algorithm (FB) in such a case, although FISTA is known to have a polynomial asymptotical convergence rate while FB is exponential. We provide a simple rule to tune the α parameter within the FISTA algorithm to reach an ε-solution with an optimal number of iterations. These new results highlight the efficiency of FISTA algorithms, and they rely on new non asymptotic bounds for FISTA.
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Dates et versions

hal-03491527 , version 1 (17-12-2021)

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  • HAL Id : hal-03491527 , version 1

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J-F Aujol, Charles Dossal, Aude Rondepierre. FISTA is an automatic geometrically optimized algorithm for strongly convex functions. 2021. ⟨hal-03491527⟩
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