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

César Gutiérrez, Enrico Miglierina, Elena Molho and Vicente Novo ()
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César Gutiérrez: Universidad de Valladolid
Enrico Miglierina: Università Cattolica del Sacro Cuore
Elena Molho: Università degli Studi di Pavia
Vicente Novo: Universidad Nacional de Educación a Distancia (UNED)

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 2, No 2, 358-371

Abstract: 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.

Keywords: Set optimization; Set relations; Minimal solutions; Stability; Set convergence; 49J53; 90C31; 90C29 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-016-0942-x

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