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

#### 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.
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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
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/709381
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