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.
Inglese
http://link.springer.com/article/10.1007%2Fs10957-016-0942-x
Gutierrez Vaquero, C., Miglierina, E., Molho, E., Novo, V., Convergence of Solutions of a Set Optimization Problem in the Image Space, <>, 2016; 170 (2): 358-371. [doi:10.1007/s10957-016-0942-x] [http://hdl.handle.net/10807/76622]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/76622
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