Axiomatization of the index of pointedness for closed convex cones



Título del documento: Axiomatization of the index of pointedness for closed convex cones
Revista: Computational & applied mathematics
Base de datos: PERIÓDICA
Número de sistema: 000268610
ISSN: 1807-0302
Autores: 1
2
Instituciones: 1Instituto de Matematica Pura e Aplicada, Rio de Janeiro. Brasil
2Universite d'Avignon, Department of Mathematics, Avignon, Vaucluse. Francia
Año:
Periodo: May-Ago
Volumen: 24
Número: 2
Paginación: 245-283
País: Brasil
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Experimental, analítico
Resumen en inglés Let C(H) denote the class of closed convex cones in a Hilbert space H. One possible way of measuring the degree of pointedness of a cone K is by evaluating the distance from K to the set of all nonpointed cones. This approach has been explored in detail in a previous work of ours. We now go beyond this particular choice and set up an axiomatic background for addressing this issue. We define an index of pointedness over H as being a function f: C(H) ® R satisfying a certain number of axioms. The number f(K) is intended, of course, to measure the degree of pointedness of the cone K. Although several important examples are discussed to illustrate the theory in action, the emphasis of this work lies in the general properties that can be derived directly from the axiomatic model
Disciplinas: Matemáticas
Palabras clave: Matemáticas aplicadas,
Conos convexos,
Conos sólidos,
Indice de precisión,
Dualidad
Keyword: Mathematics,
Applied mathematics,
Convex cones,
Solid cones,
Duality,
Pointedness index
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