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Separation of convex sets by extreme hyperplanes

✍ Scribed by A. R. Alimov, V. Yu. Protasov

Book ID: 120739272
Publisher: Springer US
Year: 2013
Tongue: English
Weight: 128 KB
Volume: 191
Category: Article
ISSN: 1573-8795
DOI: 10.1007/s10958-013-1345-2

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A convex subset K of a vector space E over the field of real numbers is linearly bounded (linearly closed) if every line intersects K in a bounded (closed) subset of the line. A hyperplane is the set of x ~ E that satisfy a linear equationf(x) = c, wherefis a linear functional and c is a real number