Generalization of the Arrow–Barankin–Blackwell Theorem in a Dual Space Setting

W. Song
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W. Song: Harbin Normal University

Journal of Optimization Theory and Applications, 1997, vol. 95, issue 1, No 11, 225-230

Abstract: Abstract In this note, we provide general sufficient conditions under which, if F is a compact [resp. w*-compact] subset of the topological dual Y* of a nonreflexive normed space Y partially ordered by a closed convex pointed cone K, then the set of points in F that can be supported by strictly positive elements in the canonical embedding of Y in Y** is norm dense [resp. w*-dense] in the efficient [maximal] point set of F. This result gives an affirmative answer to the conjecture proposed by Gallagher (Ref. 19), and also generalizes the results stated in Ref. 19 and some space specific results given in Refs. 17, 18, and 11.

Keywords: Vector optimization; efficiency; support points; density (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1022647831434

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