Arrow, Barankin and Blackwell proved in 1953 that if [special characters omitted] is given its standard partial order then for any nonempty convex compact subset A ⊂ [special characters omitted], the subset of A consisting of elements which maximize some strictly positive linear functional on A is dense in the set of Pareto efficient points of A.
This thesis presents a generalization of that theorem to locally convex Hausdorff topological vector spaces without assuming A is compact; we show asymptotic compactness is sufficient provided the asymptotic cone of A can be separated from the ordering cone by a closed, convex cone. Additionally, we give a similar generalization using Henig efficient points when A is not assumed to be convex. We show these results can be sharpened when the ordering cone has a bounded base and we show how our results can be used to obtain several results from the literature. We pay special attention to based convex cones and expansion cones in locally convex spaces.
|Advisor:||Goodrich, Robert K.|
|Commitee:||Kuznetsov, Sergei, Lewis, Clayton, Packer, Judith, Walter, Martin|
|School:||University of Colorado at Boulder|
|School Location:||United States -- Colorado|
|Source:||DAI-B 71/10, Dissertation Abstracts International|
|Subjects:||Mathematics, Theoretical Mathematics|
|Keywords:||Abb theorem, Asymptotically compact, Convex, Density, Henig efficiency, Vector optimization, Vector spaces|
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