Derivative-free optimization and filter methods to solve nonlinear constrained problems

Detalhes bibliográficos
Autor(a) principal: Correia, Aldina
Data de Publicação: 2009
Outros Autores: Matias, João, Mestre, Pedro, Serôdio, Carlos
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/1848
Resumo: In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.
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spelling Derivative-free optimization and filter methods to solve nonlinear constrained problemsNonlinear constrained optimizationFilter methodsDirect search methodsIn real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.Taylor & FrancisRepositório Científico do Instituto Politécnico do PortoCorreia, AldinaMatias, JoãoMestre, PedroSerôdio, Carlos2013-08-26T10:51:16Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/1848eng0020-716010.1080/00207160902775090info: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:RCAAP2023-03-13T12:41:19Zoai:recipp.ipp.pt:10400.22/1848Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:22:58.234578Repositório 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 Derivative-free optimization and filter methods to solve nonlinear constrained problems
title Derivative-free optimization and filter methods to solve nonlinear constrained problems
spellingShingle Derivative-free optimization and filter methods to solve nonlinear constrained problems
Correia, Aldina
Nonlinear constrained optimization
Filter methods
Direct search methods
title_short Derivative-free optimization and filter methods to solve nonlinear constrained problems
title_full Derivative-free optimization and filter methods to solve nonlinear constrained problems
title_fullStr Derivative-free optimization and filter methods to solve nonlinear constrained problems
title_full_unstemmed Derivative-free optimization and filter methods to solve nonlinear constrained problems
title_sort Derivative-free optimization and filter methods to solve nonlinear constrained problems
author Correia, Aldina
author_facet Correia, Aldina
Matias, João
Mestre, Pedro
Serôdio, Carlos
author_role author
author2 Matias, João
Mestre, Pedro
Serôdio, Carlos
author2_role author
author
author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico do Porto
dc.contributor.author.fl_str_mv Correia, Aldina
Matias, João
Mestre, Pedro
Serôdio, Carlos
dc.subject.por.fl_str_mv Nonlinear constrained optimization
Filter methods
Direct search methods
topic Nonlinear constrained optimization
Filter methods
Direct search methods
description In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-01-01T00:00:00Z
2013-08-26T10:51:16Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.22/1848
url http://hdl.handle.net/10400.22/1848
dc.language.iso.fl_str_mv eng
language eng
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10.1080/00207160902775090
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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
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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