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

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  • Michel H. Geoffroy

    (Université des Antilles)

Abstract

In this paper, we supply the power set $${\mathcal {P}}(Z)$$ 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 $${\mathcal {P}}(Z)$$ 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 $${\mathcal {P}}(Z)$$ P ( Z ) and, taking advantage of its properties, we prove several stability results for minimal sets and minimal solutions to set-valued optimization problems.

Suggested Citation

  • Michel H. Geoffroy, 2019. "A topological convergence on power sets well-suited for set optimization," Journal of Global Optimization, Springer, vol. 73(3), pages 567-581, March.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:3:d:10.1007_s10898-018-0712-4
    DOI: 10.1007/s10898-018-0712-4
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    Cited by:

    1. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Stability of efficient solutions to set optimization problems," Journal of Global Optimization, Springer, vol. 78(3), pages 563-580, November.
    2. Lam Quoc Anh & Tran Quoc Duy & Dinh Vinh Hien & Daishi Kuroiwa & Narin Petrot, 2020. "Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 416-432, May.

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