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

Michel H. Geoffroy ()
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Michel H. Geoffroy: Université des Antilles

Journal of Global Optimization, 2019, vol. 73, issue 3, No 6, 567-581

Abstract: 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.

Keywords: Set-valued optimization; Set approach; Strict ordering; Set convergence; 49J53; 65K10; 54A20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-018-0712-4

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