Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one, and their investigation has comprised several efforts from many researchers in the last decade. In this paper we focus on the convex case and, inspired by recent approaches for accelerating first-order iterative schemes, we develop a scaled inertial forward-backward algorithm which is based on a metric changing at each iteration and on a suitable extrapolation step. Unlike standard forward-backward methods with extrapolation, our scheme is able to handle functions whose domain is not the entire space. Both an O(1/k^2) convergence rate estimate on the objective function values and the convergence of the sequence of the iterates are proved. Numerical experiments on several test problems arising from image processing, compressed sensing, and statistical inference show the effectiveness of the proposed method in comparison to well-performing state-of-the-art algorithms.

A Variable Metric Forward-Backward Method with Extrapolation / Bonettini, Silvia; Porta, Federica; Ruggiero, V.. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - 38:4(2016), pp. A2558-A2584. [10.1137/15M1025098]

A Variable Metric Forward-Backward Method with Extrapolation

BONETTINI, Silvia;PORTA, FEDERICA;
2016

Abstract

Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one, and their investigation has comprised several efforts from many researchers in the last decade. In this paper we focus on the convex case and, inspired by recent approaches for accelerating first-order iterative schemes, we develop a scaled inertial forward-backward algorithm which is based on a metric changing at each iteration and on a suitable extrapolation step. Unlike standard forward-backward methods with extrapolation, our scheme is able to handle functions whose domain is not the entire space. Both an O(1/k^2) convergence rate estimate on the objective function values and the convergence of the sequence of the iterates are proved. Numerical experiments on several test problems arising from image processing, compressed sensing, and statistical inference show the effectiveness of the proposed method in comparison to well-performing state-of-the-art algorithms.
2016
38
4
A2558
A2584
A Variable Metric Forward-Backward Method with Extrapolation / Bonettini, Silvia; Porta, Federica; Ruggiero, V.. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - 38:4(2016), pp. A2558-A2584. [10.1137/15M1025098]
Bonettini, Silvia; Porta, Federica; Ruggiero, V.
File in questo prodotto:
File Dimensione Formato  
VOR_A VARIABLE METRIC FORWARD-BACKWARD METHOD.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 616.61 kB
Formato Adobe PDF
616.61 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
POST PRINT_A variable metric forward–backward method with extrapolation.pdf

Open access

Tipologia: Versione dell'autore revisionata e accettata per la pubblicazione
Dimensione 681.13 kB
Formato Adobe PDF
681.13 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1146890
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 21
  • ???jsp.display-item.citation.isi??? 20
social impact