In this work we characterize different types of solutions of a vector optimization problem by means of a scalarization procedure.Usually different scalarizing functions are used in order to obtain thevarious solutions of the vector problem. Here we consider different kinds ofsolutions of the \emph{same} scalarized problem. Our results allow us toestablish a parallelism between the solutions of the scalarized problem andthe various efficient frontiers: stronger solution concepts of the scalarproblem correspond to more restrictive notions of efficiency. Besides the usual notions of weakly efficient and efficient points, which are characterized as global (or strict global) solution of the scalarized problem, we also consider some restricted notions of efficiency, such as strict and proper efficiency, which are characterized as Tikhonov well-posed minima and sharp minima for the scalarized problem.

Degrees of efficiency and degrees of minimality / Zaffaroni, Alberto. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 42:(2003), pp. 1071-1086.

Degrees of efficiency and degrees of minimality

ZAFFARONI, Alberto
2003

Abstract

In this work we characterize different types of solutions of a vector optimization problem by means of a scalarization procedure.Usually different scalarizing functions are used in order to obtain thevarious solutions of the vector problem. Here we consider different kinds ofsolutions of the \emph{same} scalarized problem. Our results allow us toestablish a parallelism between the solutions of the scalarized problem andthe various efficient frontiers: stronger solution concepts of the scalarproblem correspond to more restrictive notions of efficiency. Besides the usual notions of weakly efficient and efficient points, which are characterized as global (or strict global) solution of the scalarized problem, we also consider some restricted notions of efficiency, such as strict and proper efficiency, which are characterized as Tikhonov well-posed minima and sharp minima for the scalarized problem.
42
1071
1086
Degrees of efficiency and degrees of minimality / Zaffaroni, Alberto. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 42:(2003), pp. 1071-1086.
Zaffaroni, Alberto
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento 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: http://hdl.handle.net/11380/709381
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 145
  • ???jsp.display-item.citation.isi??? 148
social impact