A Generalization of a Theorem of Arrow, Barankin, and Blackwell

Jahn J (1988)

Publication Type: Journal article, Original article

Publication year: 1988

Journal

SIAM Journal on Control and Optimization Society for Industrial and Applied Mathematics

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 26

Pages Range: 999-1005

Abstract

In 1953, K.J. Arrow, E.W. Barankin, and D. Blackwell proved a famous theorem concerning the density of the set of minimal solutions of strictly positive support functionals in the set of minimal elements of a compact convex subset of Rⁿ. This result has some important and interesting consequences in multi-objective optimization. But this theorem is restricted to the space Rⁿ partially ordered with respect to the componentwise ordering. In this paper, it is shown that the Arrow-Barankin-Blackwell theorem remains true in a real normed space partially ordered by a Bishop-Phelps cone.

Authors with CRIS profile

Johannes Jahn Professur für Angewandte Mathematik

How to cite

APA:

Jahn, J. (1988). A Generalization of a Theorem of Arrow, Barankin, and Blackwell. SIAM Journal on Control and Optimization, 26, 999-1005.

MLA:

Jahn, Johannes. "A Generalization of a Theorem of Arrow, Barankin, and Blackwell." SIAM Journal on Control and Optimization 26 (1988): 999-1005.

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