The Arrow-Barankin-Blackwell theorem in a dual space setting

DOI10.1007/BF02191991zbMath0823.46071MaRDI QIDQ1893336

Richard J. Gallagher

Publication date: 3 July 1995

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

vector optimizationscalarizationsupport pointsclosed convex subsettopological dualsupport functionalspartially ordered, nonreflexive normed spacestrictly positive linear functionals

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Programming in abstract spaces (90C48) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Ordered topological linear spaces, vector lattices (46A40)

Related Items (6)

A new ABB theorem in normed vector spaces ⋮ Generalization of the Arrow-Barankin-Blackwell theorem in a dual space setting ⋮ On the density of positive proper efficient points in a normed space ⋮ Generalizations of a theorem of Arrow, Barankin, and Blackwell in topological vector spaces ⋮ Maximal points of convex sets in locally convex topological vector spaces: generalization of the Arrow-Barankin-Blackwell theorem ⋮ Existence and density results for proper efficiency in cone compact sets

Cites Work

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• The structure of admissible points with respect to cone dominance
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• Ordered linear spaces
• Efficiency prices for optimal consumption plans. II
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• Positive Proper Efficient Points and Related Cone Results in Vector Optimization Theory
• The Price Equilibrium Existence Problem in Topological Vector Lattices
• Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space
• A Generalization of a Theorem of Arrow, Barankin, and Blackwell
• The geometry of Pareto efficiency over cones
• On Cone-Efficiency, Cone-Convexity and Cone-Compactness
• Two Generalizations of a Theorem of Arrow, Barankin, and Blackwell
• On the Existence of Pareto Efficient Points
• On a Question of Bishop and Phelps

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