Separation of convex sets by extreme hyperplanes

DOI10.1007/s10958-013-1345-2zbMath1280.52022OpenAlexW2007702741MaRDI QIDQ377993

Alexey R. Alimov, Vladimir Yu. Protasov

Publication date: 20 November 2013

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-013-1345-2

zbMATH Keywords

normed linear spacesseparation of convex setsextreme hyperplanes

Mathematics Subject Classification ID

Convex programming (90C25) Discrete geometry (52C99) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (7)

Connectedness and other geometric properties of suns and Chebyshev sets ⋮ Bounded strict solar property of strict suns in the space \(C(Q)\) ⋮ Continuous \(\epsilon\)-selection and monotone path-connected sets ⋮ On local properties of spaces implying monotone path-connectedness of suns ⋮ Local solarity of suns in normed linear spaces ⋮ Unnamed Item ⋮ Properties of monotone path-connected sets

Cites Work

• Unnamed Item
• An existence criterion for a smooth function under constraints
• The embedding of proximinal sets
• Suns in normed linear spaces which are finite dimensional
• Approximation properties of certain sets in the space of continuous functions
• Convex analysis and nonlinear optimization. Theory and examples
• On the extension of continuous linear functionals and best approximation in normed linear spaces
• Monotone path-connectedness of Chebyshev sets in the space $ C(Q)$
• COMBINATORIAL GEOMETRY AND CONVEXITY CLASSES
• Closed spans in vector-valued function spaces and their approximative properties

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