AUJOL, Jean-François; CALATRONI, Luca; DOSSAL, Charles; LABARRIÈRE, Hippolyte; RONDEPIERRE, Aude

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AUJOL, Jean-François
Institut de Mathématiques de Bordeaux [IMB]

CALATRONI, Luca
Morphologie et Images [MORPHEME]

DOSSAL, Charles
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]

Langue

Document de travail - Pré-publication

Ce document a été publié dans

2023-07-27

Résumé en anglais

We consider a combined restarting and adaptive backtracking strategy for the popular Fast IterativeShrinking-Thresholding Algorithm frequently employed for accelerating the convergence speed of large-scale structured convex optimization problems. Several variants of FISTA enjoy a provable linear convergence rate for the function values $F(x_n)$ of the form $\mathcal{O}( e^{-K\sqrt{\mu/L}~n})$ under the prior knowledge of problem conditioning, i.e. of the ratio between the (\L ojasiewicz) parameter $\mu$ determining the growth of the objective function and the Lipschitz constant $L$ of its smooth component. These parameters are nonetheless hard to estimate in many practical cases. Recent works address the problem by estimating either parameter via suitable adaptive strategies. In our work both parameters can be estimated at the same time by means of an algorithmic restarting scheme where, at each restart, a non-monotone estimation of $L$ is performed. For this scheme, theoretical convergence results are proved, showing that a $\mathcal{O}( e^{-K\sqrt{\mu/L}n})$ convergence speed can still be achieved along with quantitative estimates of the conditioning. The resulting Free-FISTA algorithm is therefore parameter-free. Several numerical results are reported to confirm the practical interest of its use in many exemplar problems.< Réduire

Mots clés en anglais

Composite optimization

Restart

Backtracking

Lojasiewicz property

Lipschitz constant

Acceleration

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190489

Project ANR

Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond - ANR-19-CE23-0017

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251