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Superefficiency in Local Convex Spaces

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  • J. H. Qiu

    (Suzhou University)

Abstract

In the framework of normed spaces, Borwein and Zhuang introduced superefficiency and gave its concise dual form when the underlying decision problem is convex. In this paper, we consider four different generalizations of the Borwein and Zhuang superefficiency in locally convex spaces and give their concise dual forms for convex vector optimization. When the ordering cone has a base, we clarify the relationship between Henig efficiency and the various kinds of superefficiency. Finally, we show that whether the four kinds of superefficiency are equivalent to each other depends on the normability of the underlying locally convex spaces.

Suggested Citation

  • J. H. Qiu, 2007. "Superefficiency in Local Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 19-35, October.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:1:d:10.1007_s10957-007-9211-3
    DOI: 10.1007/s10957-007-9211-3
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    References listed on IDEAS

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    1. X. Y. Zheng, 1997. "Proper Efficiency in Locally Convex Topological Vector Spaces," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 469-486, August.
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    Cited by:

    1. J. H. Qiu & Y. Hao, 2010. "Scalarization of Henig Properly Efficient Points in Locally Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 71-92, October.

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