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.
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Geoffroy, M.H. A topological convergence on power sets well-suited for set optimization. J Glob Optim 73, 567–581 (2019). https://doi.org/10.1007/s10898-018-0712-4
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DOI: https://doi.org/10.1007/s10898-018-0712-4