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

摘要

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