A new ABB theorem in normed vector spaces

DOI10.1080/02331930412331282427zbMath1055.90064OpenAlexW1978713798MaRDI QIDQ4820398

Christiane Tammer, Alfred Göpfert, Constantin Zalinescu

Publication date: 15 October 2004

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930412331282427

zbMATH Keywords

efficient pointsnormed vector space

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Programming in abstract spaces (90C48) Existence theories for problems in abstract spaces (49J27)

Related Items (7)

Density and connectedness of optimal points with respect to improvement sets ⋮ Vector optimization w.r.t. relatively solid convex cones in real linear spaces ⋮ Weak Henig proper solution sets for set optimization problems ⋮ New concept of the ABB theorem ⋮ A generalization of a theorem of Arrow, Barankin and Blackwell to a nonconvex case ⋮ Solution concepts in vector optimization: a fresh look at an old story ⋮ On the density of Henig efficient points in locally convex topological vector spaces

Cites Work

• A generalization of the Arrow-Barankin-Blackwell theorem in normed spaces
• Proper efficiency with respect to cones
• Connectedness of efficient solution sets for set-valued maps in normed spaces
• Density theorems for generalized Henig proper efficiency
• Generalization of the Arrow-Barankin-Blackwell theorem in a dual space setting
• Generalizations of a theorem of Arrow, Barankin, and Blackwell in topological vector spaces
• Variational methods in partially ordered spaces
• Maximal points of convex sets in locally convex topological vector spaces: generalization of the Arrow-Barankin-Blackwell theorem
• Comparison of existence results for efficient points
• The Arrow-Barankin-Blackwell theorem in a dual space setting
• Density of the set of positive proper minimal points in the set of minimal points
• Convexity of the optimal multifunctions and its consequences in vector optimization
• On a Theorem of Arrow, Barankin, and Blackwell
• A Generalization of a Theorem of Arrow, Barankin, and Blackwell
• Super Efficiency in Vector Optimization
• Density Results for Proper Efficiencies
• Two Generalizations of a Theorem of Arrow, Barankin, and Blackwell
• On the density of proper efficient points
• A New Abb Theorem In Banach Spaces
• Existence and density results for proper efficiency in cone compact sets

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