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.
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