ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION

Detalhes bibliográficos
Autor(a) principal: Griewank,Andreas
Data de Publicação: 2014
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Pesquisa operacional (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382014000300621
Resumo: We review the methods and applications of automatic differentiation, a research and development activity, which has evolved in various computational fields since the mid 1950's. Starting from very simple basic principles that are familiar from school, one arrives at various theoretical and practical challenges. The resulting activity encompasses mathematical research and software development; it is now oftenreferredtoas algorithmic differentiation. From a geometrical and algebraic point of view, differentiation amounts to linearization, a concept that naturally extends to infinite dimensional spaces. In contract to other surveys, we will emphasize this interpretation as it has become more important recently and also facilitates the treatment of nonsmooth problems by piecewise linearization.
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spelling ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATIONJacobiansTaylor expansionspiecewise linearizationWe review the methods and applications of automatic differentiation, a research and development activity, which has evolved in various computational fields since the mid 1950's. Starting from very simple basic principles that are familiar from school, one arrives at various theoretical and practical challenges. The resulting activity encompasses mathematical research and software development; it is now oftenreferredtoas algorithmic differentiation. From a geometrical and algebraic point of view, differentiation amounts to linearization, a concept that naturally extends to infinite dimensional spaces. In contract to other surveys, we will emphasize this interpretation as it has become more important recently and also facilitates the treatment of nonsmooth problems by piecewise linearization.Sociedade Brasileira de Pesquisa Operacional2014-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382014000300621Pesquisa Operacional v.34 n.3 2014reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/0101-7438.2014.034.03.0621info:eu-repo/semantics/openAccessGriewank,Andreaseng2014-11-12T00:00:00Zoai:scielo:S0101-74382014000300621Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2014-11-12T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false
dc.title.none.fl_str_mv ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
title ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
spellingShingle ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
Griewank,Andreas
Jacobians
Taylor expansions
piecewise linearization
title_short ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
title_full ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
title_fullStr ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
title_full_unstemmed ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
title_sort ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
author Griewank,Andreas
author_facet Griewank,Andreas
author_role author
dc.contributor.author.fl_str_mv Griewank,Andreas
dc.subject.por.fl_str_mv Jacobians
Taylor expansions
piecewise linearization
topic Jacobians
Taylor expansions
piecewise linearization
description We review the methods and applications of automatic differentiation, a research and development activity, which has evolved in various computational fields since the mid 1950's. Starting from very simple basic principles that are familiar from school, one arrives at various theoretical and practical challenges. The resulting activity encompasses mathematical research and software development; it is now oftenreferredtoas algorithmic differentiation. From a geometrical and algebraic point of view, differentiation amounts to linearization, a concept that naturally extends to infinite dimensional spaces. In contract to other surveys, we will emphasize this interpretation as it has become more important recently and also facilitates the treatment of nonsmooth problems by piecewise linearization.
publishDate 2014
dc.date.none.fl_str_mv 2014-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382014000300621
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382014000300621
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0101-7438.2014.034.03.0621
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
dc.source.none.fl_str_mv Pesquisa Operacional v.34 n.3 2014
reponame:Pesquisa operacional (Online)
instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron:SOBRAPO
instname_str Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron_str SOBRAPO
institution SOBRAPO
reponame_str Pesquisa operacional (Online)
collection Pesquisa operacional (Online)
repository.name.fl_str_mv Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
repository.mail.fl_str_mv ||sobrapo@sobrapo.org.br
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