We propose a novel generalization of the Canonical Difference of Convex problem (CDC), and we study the convergence of outer approximation algorithms for its solution, which use an approximated oracle for checking the global optimality conditions. Although the approximated optimality conditions are similar to those of CDC, this new class of problems is shown to significantly differ from its special case. Indeed, outer approximation approaches for CDC need be substantially modified in order to cope with the more general problem, bringing to new algorithms. We develop a hierarchy of conditions that guarantee global convergence, and we build three different cutting plane algorithms relying on them.

Beyond canonical DC-Optimization: the single reverse polar problem

BIGI, GIANCARLO;FRANGIONI, ANTONIO;
2012-01-01

Abstract

We propose a novel generalization of the Canonical Difference of Convex problem (CDC), and we study the convergence of outer approximation algorithms for its solution, which use an approximated oracle for checking the global optimality conditions. Although the approximated optimality conditions are similar to those of CDC, this new class of problems is shown to significantly differ from its special case. Indeed, outer approximation approaches for CDC need be substantially modified in order to cope with the more general problem, bringing to new algorithms. We develop a hierarchy of conditions that guarantee global convergence, and we build three different cutting plane algorithms relying on them.
Bigi, Giancarlo; Frangioni, Antonio; Zhang, Q.
File in questo prodotto:
File Dimensione Formato  
50/41279422167756439618880880155283054831

solo utenti autorizzati

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 718.36 kB
Formato Unknown
718.36 kB Unknown   Visualizza/Apri   Richiedi una copia
SingleReversePolar-R1.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 322.68 kB
Formato Adobe PDF
322.68 kB Adobe PDF Visualizza/Apri

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/11568/188948
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact