The present work is devoted to the study of stability in set optimization. In particular, a sequence of perturbed set optimization problems, with a fixed objective map, is studied under suitable continuity assumptions. A formulation of external and internal stability of the solutions is considered in the image space, in such a way that the convergence of a sequence of solutions of perturbed problems to a solution of the original problem is studied under appropriate compactness assumptions. Our results can also be seen as an extension to the set-valued framework of known stability results in vector optimization.

Gutierrez Vaquero, C., Miglierina, E., Molho, E., Novo, V., Convergence of Solutions of a Set Optimization Problem in the Image Space, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2016; 170 (2): 358-371. [doi:10.1007/s10957-016-0942-x] [http://hdl.handle.net/10807/76622]

Convergence of Solutions of a Set Optimization Problem in the Image Space

Gutierrez Vaquero, Cesar
Primo
;
Miglierina, Enrico
Secondo
;
2016

Abstract

The present work is devoted to the study of stability in set optimization. In particular, a sequence of perturbed set optimization problems, with a fixed objective map, is studied under suitable continuity assumptions. A formulation of external and internal stability of the solutions is considered in the image space, in such a way that the convergence of a sequence of solutions of perturbed problems to a solution of the original problem is studied under appropriate compactness assumptions. Our results can also be seen as an extension to the set-valued framework of known stability results in vector optimization.
2016
Inglese
Gutierrez Vaquero, C., Miglierina, E., Molho, E., Novo, V., Convergence of Solutions of a Set Optimization Problem in the Image Space, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2016; 170 (2): 358-371. [doi:10.1007/s10957-016-0942-x] [http://hdl.handle.net/10807/76622]
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/10807/76622
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 27
  • ???jsp.display-item.citation.isi??? 25
social impact