On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm
Autor(a) principal: | |
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Data de Publicação: | 2008 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/7714 https://doi.org/10.1007/s11075-008-9194-7 |
Resumo: | Abstract This paper is devoted to the eigenvalue complementarity problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex (Queiroz et al., Math. Comput. 73, 1849–1863, 2004). We discuss a logarithmic function and a quadratic programming formulation to find a complementarity eigenvalue by computing a stationary point of an appropriate merit function on a special convex set. A variant of the spectral projected gradient algorithm with a specially designed line search is introduced to solve the EiCP. Computational experience shows that the application of this algorithm to the logarithmic function formulation is a quite efficient way to find a solution to the symmetric EiCP. |
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On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithmAbstract This paper is devoted to the eigenvalue complementarity problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex (Queiroz et al., Math. Comput. 73, 1849–1863, 2004). We discuss a logarithmic function and a quadratic programming formulation to find a complementarity eigenvalue by computing a stationary point of an appropriate merit function on a special convex set. A variant of the spectral projected gradient algorithm with a specially designed line search is introduced to solve the EiCP. Computational experience shows that the application of this algorithm to the logarithmic function formulation is a quite efficient way to find a solution to the symmetric EiCP.2008info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/7714http://hdl.handle.net/10316/7714https://doi.org/10.1007/s11075-008-9194-7engNumerical Algorithms. 47:4 (2008) 391-407Júdice, JoaquimRaydan, MarcosRosa, SilvérioSantos, Sandrainfo: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:RCAAP2019-06-01T21:16:12Zoai:estudogeral.uc.pt:10316/7714Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:43.764509Repositório 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 |
On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm |
title |
On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm |
spellingShingle |
On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm Júdice, Joaquim |
title_short |
On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm |
title_full |
On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm |
title_fullStr |
On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm |
title_full_unstemmed |
On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm |
title_sort |
On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm |
author |
Júdice, Joaquim |
author_facet |
Júdice, Joaquim Raydan, Marcos Rosa, Silvério Santos, Sandra |
author_role |
author |
author2 |
Raydan, Marcos Rosa, Silvério Santos, Sandra |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Júdice, Joaquim Raydan, Marcos Rosa, Silvério Santos, Sandra |
description |
Abstract This paper is devoted to the eigenvalue complementarity problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex (Queiroz et al., Math. Comput. 73, 1849–1863, 2004). We discuss a logarithmic function and a quadratic programming formulation to find a complementarity eigenvalue by computing a stationary point of an appropriate merit function on a special convex set. A variant of the spectral projected gradient algorithm with a specially designed line search is introduced to solve the EiCP. Computational experience shows that the application of this algorithm to the logarithmic function formulation is a quite efficient way to find a solution to the symmetric EiCP. |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008 |
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/10316/7714 http://hdl.handle.net/10316/7714 https://doi.org/10.1007/s11075-008-9194-7 |
url |
http://hdl.handle.net/10316/7714 https://doi.org/10.1007/s11075-008-9194-7 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Numerical Algorithms. 47:4 (2008) 391-407 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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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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1799133897597911040 |