An approximate Hahn–Banach theorem for positively homogeneous functions
Contribuinte(s) |
Universidad de Alicante. Departamento de Matemáticas Laboratorio de Optimización (LOPT) |
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Data(s) |
17/03/2016
17/03/2016
2015
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Resumo |
This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p. |
Identificador |
Optimization. 2015, 64(5): 1321-1328. doi:10.1080/02331934.2013.864290 0233-1934 (Print) 1029-4945 (Online) http://hdl.handle.net/10045/53865 10.1080/02331934.2013.864290 |
Idioma(s) |
eng |
Publicador |
Taylor & Francis |
Relação |
http://dx.doi.org/10.1080/02331934.2013.864290 |
Direitos |
© 2013 Taylor & Francis info:eu-repo/semantics/restrictedAccess |
Palavras-Chave | #Approximate Hahn–Banach theorem #Non-convex Hahn–Banach theorem #Fenchel–Legendre conjugate #Positively homogeneous functions of degree one #Estadística e Investigación Operativa |
Tipo |
info:eu-repo/semantics/article |