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

K.F. Ng () and X.Y. Zheng ()
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K.F. Ng: Chinese University of Hong Kong
X.Y. Zheng: Chinese University of Hong Kong

Journal of Optimization Theory and Applications, 2002, vol. 115, issue 1, No 4, 29-47

Abstract: 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.

Keywords: Preorder; efficient points; vector optimization; support points (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1019620812169

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