Robustifying FISTA via the infinity norm of its smooth component's gradient

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Resumen

The FISTA is a well-known and fast procedure for solving optimization problems composed by the sum of two convex functions, i.e. F = f + g, such that ?f is L-Lipschitz continuous and g is possibly nonsmooth.FISTA's well-studied theoretical RoC (rate of convergence) is \mathcal{O}\left( {{k^{ - 2}}} \right); however, in the praxis, it depends on both, the extragradient rule and the step-size (SS) that estimates L. An ill-chosen SS (i.e. a large pre-defined constant), at worst, can force the objective to diverge; furthermore, some adaptive SS methods (i.e. line search, Cauchy, etc.) can slow down or force the objective to present an oscillatory behavior.In this work we present a simple add-on feature to robustify FISTA against an ill-chosen SS when F is the l1 regularized problem. It is based on modifying some entries of ?fk so as to \left\{ {{{\left\| {\nabla {f_k}} \right\|}_\infty }} \right\} is turned into a non-increasing sequence. Furthermore, tracking and limiting \left\{ {{{\left\| {\nabla {f_k}} \right\|}_\infty }} \right\} can be used (i) as an early warning method to avoid divergence k } and (ii) to allow larger or even consistently increasing SS sequences.Our computational results particularly target Convolutional Sparse Representations (CSR), where our method indeed boots FISTA's practical performance.

Idioma originalInglés
Título de la publicación alojadaConference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020
EditoresMichael B. Matthews
EditorialIEEE Computer Society
Páginas341-342
Número de páginas2
ISBN (versión digital)9780738131269
DOI
EstadoPublicada - 1 nov. 2020
Evento54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020 - Pacific Grove, Estados Unidos
Duración: 1 nov. 20205 nov. 2020

Serie de la publicación

NombreConference Record - Asilomar Conference on Signals, Systems and Computers
Volumen2020-November
ISSN (versión impresa)1058-6393

Conferencia

Conferencia54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020
País/TerritorioEstados Unidos
CiudadPacific Grove
Período1/11/205/11/20

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