We consider the convex quadratic linearly constrained problem with bounded variables and with huge and dense Hessian matrix that arises in many applications such as the training problem of bias support vector machines. We propose a decomposition algorithmic scheme suitable to parallel implementations and we prove global convergence under suitable conditions. Focusing on support vector machines training, we outline how these assumptions can be satisfied in practice and we suggest various specific implementations. Extensions of the theoretical results to general linearly constrained problem are provided. We included numerical results on support vector machines with the aim of showing the viability and the effectiveness of the proposed scheme.

Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training / Manno, Andrea; Palagi, Laura; Sagratella, Simone. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - ELETTRONICO. - 71:1(2018), pp. 115-145. [10.1007/s10589-018-9987-0]

Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training

Andrea Manno
Writing – Original Draft Preparation
;
Laura Palagi
;
Simone Sagratella
Writing – Original Draft Preparation
2018

Abstract

We consider the convex quadratic linearly constrained problem with bounded variables and with huge and dense Hessian matrix that arises in many applications such as the training problem of bias support vector machines. We propose a decomposition algorithmic scheme suitable to parallel implementations and we prove global convergence under suitable conditions. Focusing on support vector machines training, we outline how these assumptions can be satisfied in practice and we suggest various specific implementations. Extensions of the theoretical results to general linearly constrained problem are provided. We included numerical results on support vector machines with the aim of showing the viability and the effectiveness of the proposed scheme.
2018
Decomposition algorithm; Big data; Support vector machines; Parallel computing
01 Pubblicazione su rivista::01a Articolo in rivista
Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training / Manno, Andrea; Palagi, Laura; Sagratella, Simone. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - ELETTRONICO. - 71:1(2018), pp. 115-145. [10.1007/s10589-018-9987-0]
File allegati a questo prodotto
File Dimensione Formato  
Manno_Preprint_Parallel-Decomposition_2018.pdf

accesso aperto

Note: https://link.springer.com/article/10.1007/s10589-018-9987-0
Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.98 MB
Formato Adobe PDF
1.98 MB Adobe PDF
Manno_Parallel-Decomposition_2018.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.12 MB
Formato Adobe PDF
1.12 MB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1071021
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 8
social impact