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Título:
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Every closed convex set is the set of minimizers of some C1-smooth convex function
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Autores:
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Azagra Rueda, Daniel ;
Ferrera Cuesta, Juan
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Tipo de documento:
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texto impreso
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Editorial:
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America Mathematical Society, 2002
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Análisis funcional y teoría de operadores
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Tipo = Artículo
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Resumen:
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The authors show that for every closed convex set C in a separable Banach space there is a nonnegative C1 convex function f such that C = {x: f(x) = 0}. The key is to show this for a closed halfspace. This result has several attractive consequences. For example, it provides an easy proof that every closed convex set is the Hausdorff limit of infinitely smooth convex bodies (Cn := {x: f(x) _ 1/n}) and that every continuous convex function is the Mosco limit of C1 convex functions.
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En línea:
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https://eprints.ucm.es/id/eprint/12354/1/2002every1.pdf
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