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On the Density of Henig Efficient Points in Locally Convex Topological Vector Spaces

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  • Joseph Newhall

    (Zayed University)

  • Robert K. Goodrich

    (University of Colorado)

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.

Suggested Citation

  • Joseph Newhall & Robert K. Goodrich, 2015. "On the Density of Henig Efficient Points in Locally Convex Topological Vector Spaces," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 753-762, June.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:3:d:10.1007_s10957-014-0644-1
    DOI: 10.1007/s10957-014-0644-1
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    References listed on IDEAS

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    1. L.W. Woo & R.K. Goodrich, 2003. "Maximal Points of Convex Sets in Locally Convex Topological Vector Spaces: Generalization of the Arrow–Barankin–Blackwell Theorem," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 647-658, March.
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