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Existence of Efficient Points in Vector Optimization and Generalized Bishop–Phelps Theorem

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  • K.F. Ng

    (Chinese University of Hong Kong)

  • X.Y. Zheng

    (Chinese University of Hong Kong)

Abstract

In a set without linear structure equipped with a preorder, we give a general existence result for efficient points. In a topological vector space equipped with a partial order induced by a closed convex cone with a bounded base, we prove another kind of existence result for efficient points; this result does not depend on the Zorn lemma. As applications, we study a solution problem in vector optimization and generalize the Bishop–Phelps theorem to a topological vector space setting by showing that the B-support points of any sequentially complete closed subset A of a topological vector space E is dense in ∂A, where B is any bounded convex subset of E.

Suggested Citation

  • K.F. Ng & X.Y. Zheng, 2002. "Existence of Efficient Points in Vector Optimization and Generalized Bishop–Phelps Theorem," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 29-47, October.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:1:d:10.1023_a:1019620812169
    DOI: 10.1023/A:1019620812169
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    References listed on IDEAS

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    1. Jonathan M. Borwein, 1983. "On the Existence of Pareto Efficient Points," Mathematics of Operations Research, INFORMS, vol. 8(1), pages 64-73, February.
    2. Dinh The Luc, 1989. "An Existence Theorem in Vector Optimization," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 693-699, November.
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    Cited by:

    1. Nergiz Kasimbeyli, 2015. "Existence and characterization theorems in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 62(1), pages 155-165, May.

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