ON AUTOMATIC DIFFERENTIATION AND ALGORITHMIC LINEARIZATION
Autor(a) principal: | |
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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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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 |
_version_ |
1750318017769635840 |