The aim of this paper is to extend some notions of proper minimality from vector optimization to set optimization. In particular, we focus our attention on the concepts of Henig and Geoffrion proper minimality, which are well-known in vector optimization. We introduce a generalization of both of them in set optimization with finite dimensional spaces, by considering also a special class of polyhedral ordering cone. In this framework, we prove that these two notions are equivalent, as it happens in the vector optimization context, where this property is well-known. Then, we study a characterization of these proper minimal points through nonlinear scalarization, without considering convexity hypotheses.

Huerga, L., Miglierina, E., Molho, E., Novo, V., On proper minimality in set optimization, <<OPTIMIZATION LETTERS>>, N/A; (N/A): N/A-N/A. [doi:10.1007/s11590-023-02005-9] [https://hdl.handle.net/10807/235830]

On proper minimality in set optimization

Miglierina, Enrico;
2023

Abstract

The aim of this paper is to extend some notions of proper minimality from vector optimization to set optimization. In particular, we focus our attention on the concepts of Henig and Geoffrion proper minimality, which are well-known in vector optimization. We introduce a generalization of both of them in set optimization with finite dimensional spaces, by considering also a special class of polyhedral ordering cone. In this framework, we prove that these two notions are equivalent, as it happens in the vector optimization context, where this property is well-known. Then, we study a characterization of these proper minimal points through nonlinear scalarization, without considering convexity hypotheses.
2023
Inglese
Huerga, L., Miglierina, E., Molho, E., Novo, V., On proper minimality in set optimization, <<OPTIMIZATION LETTERS>>, N/A; (N/A): N/A-N/A. [doi:10.1007/s11590-023-02005-9] [https://hdl.handle.net/10807/235830]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/10807/235830
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact