Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals

Detalhes bibliográficos
Autor(a) principal: Goncharov, Vladimir
Data de Publicação: 2011
Outros Autores: Pereira, Fatima
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10174/2491
Resumo: For a closed subset C of a Hilbert space and for a sublinear functional, which is equivalent to the norm, we give conditions guaranteeing existence and uniqueness of the nearest points to C in the sense of the semidistance generated by given sublinear functional. This permits us to construct a continuous retraction onto C well defined in an open neighbourhood of C. In particular, according to one of the conditions, this neighbourhood can be represented in terms of balance between the local strict convexity modulus of the Minkowski (sublinear) functional and the measure of nonconvexity of the set C at each point.
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spelling Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionalsTime-minimum problemMinkowski functionalgeneralized projectionstrict convexitycurvatureproximal normalsFor a closed subset C of a Hilbert space and for a sublinear functional, which is equivalent to the norm, we give conditions guaranteeing existence and uniqueness of the nearest points to C in the sense of the semidistance generated by given sublinear functional. This permits us to construct a continuous retraction onto C well defined in an open neighbourhood of C. In particular, according to one of the conditions, this neighbourhood can be represented in terms of balance between the local strict convexity modulus of the Minkowski (sublinear) functional and the measure of nonconvexity of the set C at each point.Heldermann Verlag2011-01-24T16:36:23Z2011-01-242011-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article330605 bytesapplication/pdfhttp://hdl.handle.net/10174/2491http://hdl.handle.net/10174/2491engpag 1-360944-653218Journal of Convex Analysis1livregoncha@uevora.ptfmfp@uevora.pt334Goncharov, VladimirPereira, Fatimainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T18:39:02Zoai:dspace.uevora.pt:10174/2491Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:58:12.119890Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals
title Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals
spellingShingle Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals
Goncharov, Vladimir
Time-minimum problem
Minkowski functional
generalized projection
strict convexity
curvature
proximal normals
title_short Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals
title_full Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals
title_fullStr Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals
title_full_unstemmed Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals
title_sort Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals
author Goncharov, Vladimir
author_facet Goncharov, Vladimir
Pereira, Fatima
author_role author
author2 Pereira, Fatima
author2_role author
dc.contributor.author.fl_str_mv Goncharov, Vladimir
Pereira, Fatima
dc.subject.por.fl_str_mv Time-minimum problem
Minkowski functional
generalized projection
strict convexity
curvature
proximal normals
topic Time-minimum problem
Minkowski functional
generalized projection
strict convexity
curvature
proximal normals
description For a closed subset C of a Hilbert space and for a sublinear functional, which is equivalent to the norm, we give conditions guaranteeing existence and uniqueness of the nearest points to C in the sense of the semidistance generated by given sublinear functional. This permits us to construct a continuous retraction onto C well defined in an open neighbourhood of C. In particular, according to one of the conditions, this neighbourhood can be represented in terms of balance between the local strict convexity modulus of the Minkowski (sublinear) functional and the measure of nonconvexity of the set C at each point.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-24T16:36:23Z
2011-01-24
2011-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10174/2491
http://hdl.handle.net/10174/2491
url http://hdl.handle.net/10174/2491
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv pag 1-36
0944-6532
18
Journal of Convex Analysis
1
livre
goncha@uevora.pt
fmfp@uevora.pt
334
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 330605 bytes
application/pdf
dc.publisher.none.fl_str_mv Heldermann Verlag
publisher.none.fl_str_mv Heldermann Verlag
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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