Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets

Detalhes bibliográficos
Autor(a) principal: Kostyukova, O. I.
Data de Publicação: 2019
Outros Autores: Tchemisova, T. V.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/25231
Resumo: The concepts of immobile indices and their immobility orders are objective and important characteristics of feasible sets of semi-infinite programming (SIP) problems. They can be used for the formulation of new efficient optimality conditions without constraint qualifications. Given a class of convex SIP problems with polyhedral index sets, we describe and justify a finite constructive algorithm (algorithm DIIPS) that allows to find in a finite number of steps all immobile indices and the corresponding immobility orders along the feasible directions. This algorithm is based on a representation of the cones of feasible directions in the polyhedral index sets in the form of linear combinations of extremal rays and on the approach proposed in our previous papers for the cases of immobile indices’ sets of simpler structures. A constructive procedure of determination of the extremal rays is described, and an example illustrating the application of the DIIPS algorithm is provided.
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spelling Algorithmic determination of immobile indices in convex SIP problems with polyhedral index setsSemi-infinite programming (SIP)Convex programming (CP)Immobile indexImmobility orderCone of feasible directionsExtremal rayThe concepts of immobile indices and their immobility orders are objective and important characteristics of feasible sets of semi-infinite programming (SIP) problems. They can be used for the formulation of new efficient optimality conditions without constraint qualifications. Given a class of convex SIP problems with polyhedral index sets, we describe and justify a finite constructive algorithm (algorithm DIIPS) that allows to find in a finite number of steps all immobile indices and the corresponding immobility orders along the feasible directions. This algorithm is based on a representation of the cones of feasible directions in the polyhedral index sets in the form of linear combinations of extremal rays and on the approach proposed in our previous papers for the cases of immobile indices’ sets of simpler structures. A constructive procedure of determination of the extremal rays is described, and an example illustrating the application of the DIIPS algorithm is provided.Taylor & Francis2019-02-06T14:51:09Z2020-01-01T00:00:00Z2020info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/25231eng0315-598610.1080/03155986.2018.1553754Kostyukova, O. I.Tchemisova, T. V.info: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:RCAAP2024-02-22T11:48:59Zoai:ria.ua.pt:10773/25231Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:58:32.882094Repositório 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 Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets
title Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets
spellingShingle Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets
Kostyukova, O. I.
Semi-infinite programming (SIP)
Convex programming (CP)
Immobile index
Immobility order
Cone of feasible directions
Extremal ray
title_short Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets
title_full Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets
title_fullStr Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets
title_full_unstemmed Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets
title_sort Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets
author Kostyukova, O. I.
author_facet Kostyukova, O. I.
Tchemisova, T. V.
author_role author
author2 Tchemisova, T. V.
author2_role author
dc.contributor.author.fl_str_mv Kostyukova, O. I.
Tchemisova, T. V.
dc.subject.por.fl_str_mv Semi-infinite programming (SIP)
Convex programming (CP)
Immobile index
Immobility order
Cone of feasible directions
Extremal ray
topic Semi-infinite programming (SIP)
Convex programming (CP)
Immobile index
Immobility order
Cone of feasible directions
Extremal ray
description The concepts of immobile indices and their immobility orders are objective and important characteristics of feasible sets of semi-infinite programming (SIP) problems. They can be used for the formulation of new efficient optimality conditions without constraint qualifications. Given a class of convex SIP problems with polyhedral index sets, we describe and justify a finite constructive algorithm (algorithm DIIPS) that allows to find in a finite number of steps all immobile indices and the corresponding immobility orders along the feasible directions. This algorithm is based on a representation of the cones of feasible directions in the polyhedral index sets in the form of linear combinations of extremal rays and on the approach proposed in our previous papers for the cases of immobile indices’ sets of simpler structures. A constructive procedure of determination of the extremal rays is described, and an example illustrating the application of the DIIPS algorithm is provided.
publishDate 2019
dc.date.none.fl_str_mv 2019-02-06T14:51:09Z
2020-01-01T00:00:00Z
2020
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/10773/25231
url http://hdl.handle.net/10773/25231
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0315-5986
10.1080/03155986.2018.1553754
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
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
repository.mail.fl_str_mv
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