Abstract
This paper presents a generalization of the Arrow, Barankin and Blackwell theorem to locally convex Hausdorff topological vector spaces. Our main result relaxes the requirement that the objective set be compact; we show asymptotic compactness is sufficient, provided the asymptotic cone of the objective set can be separated from the ordering cone by a closed and convex cone. Additionally, we give a similar generalization using Henig efficient points when the objective set is not assumed to be convex. Our results generalize results of A. Göpfert, C. Tammer, and C. Zălinescu to locally convex spaces.
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Acknowledgments
We would like to thank the anonymous referees for their many helpful suggestions to improve earlier versions of this paper.
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Communicated by Jonathan Borwein.
Based on the Ph.D. Dissertation of Joseph Newhall.
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Newhall, J., Goodrich, R.K. On the Density of Henig Efficient Points in Locally Convex Topological Vector Spaces. J Optim Theory Appl 165, 753–762 (2015). https://doi.org/10.1007/s10957-014-0644-1
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DOI: https://doi.org/10.1007/s10957-014-0644-1
Keywords
- Henig efficient point
- Regular efficient point
- Asymptotic cone
- Asymptotically compact set
- Density results