A set-valued gap function, g, existing in the literature for smooth and nonsmooth multiobjective optimization problems is dealt with. It is known that 0 € d(1*)is a sufficient condition forefficiency of a feasible solution r*, while the converse does not hold. In the current work, the converse of this assertion is proved for properly efficient solutions. Afterwards, to avoid the complexities of set-valued maps some new single-valued gap functions, for nonsmooth multiobjective optimization problems with locally Lipschitz data are introduced. Important properties of the new gap functions are established.
On gap functions for nonsmooth multiobjective optimization problems
Caristi, GiuseppePrimo
;
2018-01-01
Abstract
A set-valued gap function, g, existing in the literature for smooth and nonsmooth multiobjective optimization problems is dealt with. It is known that 0 € d(1*)is a sufficient condition forefficiency of a feasible solution r*, while the converse does not hold. In the current work, the converse of this assertion is proved for properly efficient solutions. Afterwards, to avoid the complexities of set-valued maps some new single-valued gap functions, for nonsmooth multiobjective optimization problems with locally Lipschitz data are introduced. Important properties of the new gap functions are established.File | Dimensione | Formato | |
---|---|---|---|
nader 4.pdf
solo utenti autorizzati
Descrizione: Articolo
Tipologia:
Versione Editoriale (PDF)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
4.24 MB
Formato
Adobe PDF
|
4.24 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
3104019.pdf
solo utenti autorizzati
Descrizione: Articolo
Tipologia:
Versione Editoriale (PDF)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
6.89 MB
Formato
Adobe PDF
|
6.89 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.