Jahn J (1988)
Publication Type: Journal article, Original article
Publication year: 1988
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 26
Pages Range: 999-1005
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.
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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