Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points

Detalhes bibliográficos
Autor(a) principal: Kostyukova, O. I.
Data de Publicação: 2005
Outros Autores: Tchemisova, T. V., Yermalinskaya, S. A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/6241
Resumo: The paper deals with convex Semi-In¯nite Programming (SIP) problems. A new concept of immobility order is introduced and an algorithm of determination of the immobility orders (DIO algorithm) and so called immobile points is suggested. It is shown that in the presence of the immobile points SIP problems do not satisfy the Slater condition. Given convex SIP problem, we determine all its immobile points and use them to formulate a Nonlinear Programming (NLP) problem in a special form. It is proved that optimality conditions for the (in¯nite) SIP problem can be formulated in terms of the analogous conditions for the corresponding (¯nite) NLP problem. The main result of the paper is the Implicit Optimality Criterion that permits to obtain new e±cient optimality conditions for the convex SIP problems (even not satisfying the Slater condition) using the known results of the optimality theory of NLP.
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spelling Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile pointsSemi-infinite programmingNonlinear programmingThe Slater conditionOptimality criterionThe paper deals with convex Semi-In¯nite Programming (SIP) problems. A new concept of immobility order is introduced and an algorithm of determination of the immobility orders (DIO algorithm) and so called immobile points is suggested. It is shown that in the presence of the immobile points SIP problems do not satisfy the Slater condition. Given convex SIP problem, we determine all its immobile points and use them to formulate a Nonlinear Programming (NLP) problem in a special form. It is proved that optimality conditions for the (in¯nite) SIP problem can be formulated in terms of the analogous conditions for the corresponding (¯nite) NLP problem. The main result of the paper is the Implicit Optimality Criterion that permits to obtain new e±cient optimality conditions for the convex SIP problems (even not satisfying the Slater condition) using the known results of the optimality theory of NLP.Universidade de Aveiro2012-02-10T17:16:07Z2005-01-01T00:00:00Z2005info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/6241engKostyukova, O. I.Tchemisova, T. V.Yermalinskaya, S. A.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:RCAAP2024-02-22T11:10:34Zoai:ria.ua.pt:10773/6241Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:44:18.665100Repositório 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 Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points
title Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points
spellingShingle Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points
Kostyukova, O. I.
Semi-infinite programming
Nonlinear programming
The Slater condition
Optimality criterion
title_short Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points
title_full Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points
title_fullStr Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points
title_full_unstemmed Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points
title_sort Convex semi-infinite programming: implicit optimality criterion based on the concept of immobile points
author Kostyukova, O. I.
author_facet Kostyukova, O. I.
Tchemisova, T. V.
Yermalinskaya, S. A.
author_role author
author2 Tchemisova, T. V.
Yermalinskaya, S. A.
author2_role author
author
dc.contributor.author.fl_str_mv Kostyukova, O. I.
Tchemisova, T. V.
Yermalinskaya, S. A.
dc.subject.por.fl_str_mv Semi-infinite programming
Nonlinear programming
The Slater condition
Optimality criterion
topic Semi-infinite programming
Nonlinear programming
The Slater condition
Optimality criterion
description The paper deals with convex Semi-In¯nite Programming (SIP) problems. A new concept of immobility order is introduced and an algorithm of determination of the immobility orders (DIO algorithm) and so called immobile points is suggested. It is shown that in the presence of the immobile points SIP problems do not satisfy the Slater condition. Given convex SIP problem, we determine all its immobile points and use them to formulate a Nonlinear Programming (NLP) problem in a special form. It is proved that optimality conditions for the (in¯nite) SIP problem can be formulated in terms of the analogous conditions for the corresponding (¯nite) NLP problem. The main result of the paper is the Implicit Optimality Criterion that permits to obtain new e±cient optimality conditions for the convex SIP problems (even not satisfying the Slater condition) using the known results of the optimality theory of NLP.
publishDate 2005
dc.date.none.fl_str_mv 2005-01-01T00:00:00Z
2005
2012-02-10T17:16:07Z
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/10773/6241
url http://hdl.handle.net/10773/6241
dc.language.iso.fl_str_mv eng
language eng
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 Universidade de Aveiro
publisher.none.fl_str_mv Universidade de Aveiro
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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