The recent literature on first order methods for smooth optimization shows that significant improvements on the practical convergence behavior can be achieved with variable step size and scaling for the gradient, making this class of algorithms attractive for a variety of relevant applications. In this paper we introduce a variable metric in the context of the -subgradient methods for nonsmooth, convex problems, in combination with two different step size selection strategies. We develop the theoretical convergence analysis of the proposed approach in the general framework of forward-backward -subgradient splitting methods and we also discuss practical implementation issues. In order to illustrate the effectiveness of the method, we consider a specific problem in the image restoration framework and we numerically evaluate the effects of a variable scaling and of the step length selection strategy on the convergence behavior.

Scaling techniques for $epsilon$-subgradient methods / Bonettini, Silvia; Benfenati, Alessandro; Ruggiero, Valeria. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - 26:3(2016), pp. 1741-1772. [10.1137/14097642X]

Scaling techniques for $epsilon$-subgradient methods

BONETTINI, Silvia;
2016

Abstract

The recent literature on first order methods for smooth optimization shows that significant improvements on the practical convergence behavior can be achieved with variable step size and scaling for the gradient, making this class of algorithms attractive for a variety of relevant applications. In this paper we introduce a variable metric in the context of the -subgradient methods for nonsmooth, convex problems, in combination with two different step size selection strategies. We develop the theoretical convergence analysis of the proposed approach in the general framework of forward-backward -subgradient splitting methods and we also discuss practical implementation issues. In order to illustrate the effectiveness of the method, we consider a specific problem in the image restoration framework and we numerically evaluate the effects of a variable scaling and of the step length selection strategy on the convergence behavior.
2016
26
3
1741
1772
Scaling techniques for $epsilon$-subgradient methods / Bonettini, Silvia; Benfenati, Alessandro; Ruggiero, Valeria. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - 26:3(2016), pp. 1741-1772. [10.1137/14097642X]
Bonettini, Silvia; Benfenati, Alessandro; Ruggiero, Valeria
File in questo prodotto:
File Dimensione Formato  
VOR_Scaling Techniques.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 1.16 MB
Formato Adobe PDF
1.16 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
POST PRINT_Scaling techniques for.pdf

Open access

Tipologia: Versione dell'autore revisionata e accettata per la pubblicazione
Dimensione 619.46 kB
Formato Adobe PDF
619.46 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/11380/1146889
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 13
social impact