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Journal of Global Optimization

, Volume 73, Issue 3, pp 567–581 | Cite as

A topological convergence on power sets well-suited for set optimization

  • Michel H. GeoffroyEmail author
Article
  • 136 Downloads

Abstract

In this paper, we supply the power set \({\mathcal {P}}(Z)\) of a partially ordered normed space Z with a transitive and irreflexive binary relation which allows us to introduce a notion of open intervals on \({\mathcal {P}}(Z)\) from which we construct a topology on the set of lower bounded subsets of Z. From this topology, we derive a concept of set convergence that is compatible with the strict ordering on \({\mathcal {P}}(Z)\) and, taking advantage of its properties, we prove several stability results for minimal sets and minimal solutions to set-valued optimization problems.

Keywords

Set-valued optimization Set approach Strict ordering Set convergence 

Mathematics Subject Classification

49J53 65K10 54A20 

Notes

Acknowledgements

The author would like to thank the anonymous referee for his/her careful reading of the manuscript and for providing valuable and accurate comments.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.LAMIA, Department of MathematicsUniversité des AntillesPointe-à-PitreFrance

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