This paper aims to study how much ``generalized'' invex properties differ from invexity and to establish whether or not the use of more and more parameters and functionals in the definitions is really effective and helpful. In particular, both smooth and nonsmooth scalar functions are considered. As a conclusion, by means of some equivalence results not necessarily related to invexity, it is proved that several ``generalized'' invexity properties are actually equivalent to invexity, and that this happens in both the differentiable case and the nondifferentiable one. In other words, the introduction of parameters in defining scalar ``generalized'' invexity properties does not yield ``a priori" any kind of generalization.
A note on scalar “generalized” invexity
carosi laura;cambini riccardo
2019-01-01
Abstract
This paper aims to study how much ``generalized'' invex properties differ from invexity and to establish whether or not the use of more and more parameters and functionals in the definitions is really effective and helpful. In particular, both smooth and nonsmooth scalar functions are considered. As a conclusion, by means of some equivalence results not necessarily related to invexity, it is proved that several ``generalized'' invexity properties are actually equivalent to invexity, and that this happens in both the differentiable case and the nondifferentiable one. In other words, the introduction of parameters in defining scalar ``generalized'' invexity properties does not yield ``a priori" any kind of generalization.File | Dimensione | Formato | |
---|---|---|---|
JIOS-T-416 final galley proof.pdf
solo utenti autorizzati
Descrizione: Articolo principale
Tipologia:
Documento in Pre-print
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
201.51 kB
Formato
Adobe PDF
|
201.51 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
CambiniCarosi_Invexity.pdf
Open Access dal 29/09/2020
Tipologia:
Documento in Post-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
245.09 kB
Formato
Adobe PDF
|
245.09 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.