Axiomatization of the index of pointedness for closed convex cones
Autor(a) principal: | |
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Data de Publicação: | 2005 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022005000200006 |
Resumo: | 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. |
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Axiomatization of the index of pointedness for closed convex conespointed conesolid coneindex of pointednessdualityLet 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.Sociedade Brasileira de Matemática Aplicada e Computacional2005-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022005000200006Computational & Applied Mathematics v.24 n.2 2005reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S0101-82052005000200006info:eu-repo/semantics/openAccessIusem,AlfredoSeeger,Albertoeng2005-11-07T00:00:00Zoai:scielo:S1807-03022005000200006Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2005-11-07T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false |
dc.title.none.fl_str_mv |
Axiomatization of the index of pointedness for closed convex cones |
title |
Axiomatization of the index of pointedness for closed convex cones |
spellingShingle |
Axiomatization of the index of pointedness for closed convex cones Iusem,Alfredo pointed cone solid cone index of pointedness duality |
title_short |
Axiomatization of the index of pointedness for closed convex cones |
title_full |
Axiomatization of the index of pointedness for closed convex cones |
title_fullStr |
Axiomatization of the index of pointedness for closed convex cones |
title_full_unstemmed |
Axiomatization of the index of pointedness for closed convex cones |
title_sort |
Axiomatization of the index of pointedness for closed convex cones |
author |
Iusem,Alfredo |
author_facet |
Iusem,Alfredo Seeger,Alberto |
author_role |
author |
author2 |
Seeger,Alberto |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Iusem,Alfredo Seeger,Alberto |
dc.subject.por.fl_str_mv |
pointed cone solid cone index of pointedness duality |
topic |
pointed cone solid cone index of pointedness duality |
description |
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. |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005-08-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022005000200006 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022005000200006 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0101-82052005000200006 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
dc.source.none.fl_str_mv |
Computational & Applied Mathematics v.24 n.2 2005 reponame:Computational & Applied Mathematics instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) instacron:SBMAC |
instname_str |
Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
instacron_str |
SBMAC |
institution |
SBMAC |
reponame_str |
Computational & Applied Mathematics |
collection |
Computational & Applied Mathematics |
repository.name.fl_str_mv |
Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
repository.mail.fl_str_mv |
||sbmac@sbmac.org.br |
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1754734889736863744 |