Berge’s theorem for noncompact image sets
By Eugene A. Feinberg, P. Kasyanov, N. V. Zadoianchuk. 2012
84 citations recorded by the source corpus.
Abstract For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined on the product of these spaces, Berge’s theorem states lower semi-continuity of the minimum of this function taken over the image sets. It assumes that the image sets are compact. For Hausdorff topological spaces, this paper extends Berge’s theorem to set-valued mappings with possible noncompact image sets and studies relevant properties of minima.
Subfields: Algebra and Number Theory, Geometry and Topology, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/e8dd0d3c42e354e9de829819eb3ff3760ccb7c4e
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In Algebra and Number Theory
In Geometry and Topology
In Management Science and Operations Research
Citations in the corpus
- Bergeʼs maximum theorem for noncompact image sets (2013, background): “[7] are proved there, in fact, for KN-inf-compact functions u.”
- Optimality Conditions for Inventory Control (2016, background): “ are important for control theory, games, and mathematical economics. The major limitation of these theorems is that they require compact action sets. The generalizations provided in Feinberg et al., [26, 28] remove this limitation. Here we present these results for metric spaces. With slight modica”