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, CesarPrimo
;Miglierina, EnricoSecondo
;
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.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
