Métodos de primeira ordem acelerados

Detalhes bibliográficos
Autor(a) principal: Ribeiro, Douglas Nascimento
Data de Publicação: 2022
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
dARK ID: ark:/38995/0013000004v6m
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/12377
Resumo: The analysis of the efficiency of algorithms to solve optimization problems is fundamental for the improvement and design of algorithms with better computational performances. Such efficiency can be measured, for example, by the “speed” in which the sequence generated by the algorithm converges to a solution of the problem at hand. From the work of Nesterov and Nemirovski in the 80's, the efficiency of an algorithm was also considered through its iteration complexity, that is, the number of iterations necessary to obtain an "approximate solution" for the problem. In this work, we will analyze the iteration complexity of the algorithms: Iterative Shrinkage-Thresholding (ISTA), Fast Iterative Shrinkage-Thresholding (FISTA) and an accelerated Forward-Backward Nesterov type method. This study will be be carried out from a theoretical and computational point of view.
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spelling Melo, Jefferson Divino Gonçalves dehttp://lattes.cnpq.br/8296171010616435Melo, Jefferson Divino Gonçalves deAlves, Maicon MarquesGonçalves, Max Leandro NobreFerreira, Orizon Pereirahttp://lattes.cnpq.br/7276599246999990Ribeiro, Douglas Nascimento2022-10-18T13:04:16Z2022-10-18T13:04:16Z2022-08-18RIBEIRO, D. N. Métodos de primeira ordem acelerados. 2022. 70 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.http://repositorio.bc.ufg.br/tede/handle/tede/12377ark:/38995/0013000004v6mThe analysis of the efficiency of algorithms to solve optimization problems is fundamental for the improvement and design of algorithms with better computational performances. Such efficiency can be measured, for example, by the “speed” in which the sequence generated by the algorithm converges to a solution of the problem at hand. From the work of Nesterov and Nemirovski in the 80's, the efficiency of an algorithm was also considered through its iteration complexity, that is, the number of iterations necessary to obtain an "approximate solution" for the problem. In this work, we will analyze the iteration complexity of the algorithms: Iterative Shrinkage-Thresholding (ISTA), Fast Iterative Shrinkage-Thresholding (FISTA) and an accelerated Forward-Backward Nesterov type method. This study will be be carried out from a theoretical and computational point of view.A análise da eficiência de algoritmos para resolver problemas de otimização é fundamental para o aprimoramento e elaboração de algoritmos com melhor desempenho computacional. Tal eficiência pode ser mensurada, por exemplo, pela “velocidade” com que a sequência gerada pelo algoritmo converge para uma solução do problema em questão, ou seja, a taxa de convergência assintótica (convergência sublinear, linear ou quadrática, etc). A partir dos trabalhos de Nesterov e Nemirovski na década de 80, a eficiência de um algoritmo passou também a ser considerada por meio de sua complexidade por iteração, isto é, o número de iterações necessárias para obter uma “solução aproximada” do problema de interesse. Neste trabalho, iremos analisar a complexidade por iteração dos algoritmos Iterative Shrinkage-Thresholding (ISTA), Fast Iterative Shrinkage-Thresholding (FISTA) e um método acelerado Forward-Backward de Nesterov. Este estudo será feito do ponto de vista teórico e computacional.Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2022-10-17T18:58:58Z No. of bitstreams: 2 Dissertação - Douglas Nascimento Ribeiro - 2022.pdf: 4065145 bytes, checksum: ead4d4137507c781c517227d1fce7470 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2022-10-18T13:04:16Z (GMT) No. of bitstreams: 2 Dissertação - Douglas Nascimento Ribeiro - 2022.pdf: 4065145 bytes, checksum: ead4d4137507c781c517227d1fce7470 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5)Made available in DSpace on 2022-10-18T13:04:16Z (GMT). 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dc.title.pt_BR.fl_str_mv Métodos de primeira ordem acelerados
dc.title.alternative.eng.fl_str_mv Accelerated first oder methods
title Métodos de primeira ordem acelerados
spellingShingle Métodos de primeira ordem acelerados
Ribeiro, Douglas Nascimento
ISTA
FISTA
Método acelerado forward – backward
Complexidade por iteração
Accelerated forward – backward
Iteration complexity
CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA
title_short Métodos de primeira ordem acelerados
title_full Métodos de primeira ordem acelerados
title_fullStr Métodos de primeira ordem acelerados
title_full_unstemmed Métodos de primeira ordem acelerados
title_sort Métodos de primeira ordem acelerados
author Ribeiro, Douglas Nascimento
author_facet Ribeiro, Douglas Nascimento
author_role author
dc.contributor.advisor1.fl_str_mv Melo, Jefferson Divino Gonçalves de
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/8296171010616435
dc.contributor.referee1.fl_str_mv Melo, Jefferson Divino Gonçalves de
dc.contributor.referee2.fl_str_mv Alves, Maicon Marques
dc.contributor.referee3.fl_str_mv Gonçalves, Max Leandro Nobre
dc.contributor.referee4.fl_str_mv Ferreira, Orizon Pereira
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/7276599246999990
dc.contributor.author.fl_str_mv Ribeiro, Douglas Nascimento
contributor_str_mv Melo, Jefferson Divino Gonçalves de
Melo, Jefferson Divino Gonçalves de
Alves, Maicon Marques
Gonçalves, Max Leandro Nobre
Ferreira, Orizon Pereira
dc.subject.por.fl_str_mv ISTA
FISTA
Método acelerado forward – backward
Complexidade por iteração
topic ISTA
FISTA
Método acelerado forward – backward
Complexidade por iteração
Accelerated forward – backward
Iteration complexity
CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA
dc.subject.eng.fl_str_mv Accelerated forward – backward
Iteration complexity
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA
description The analysis of the efficiency of algorithms to solve optimization problems is fundamental for the improvement and design of algorithms with better computational performances. Such efficiency can be measured, for example, by the “speed” in which the sequence generated by the algorithm converges to a solution of the problem at hand. From the work of Nesterov and Nemirovski in the 80's, the efficiency of an algorithm was also considered through its iteration complexity, that is, the number of iterations necessary to obtain an "approximate solution" for the problem. In this work, we will analyze the iteration complexity of the algorithms: Iterative Shrinkage-Thresholding (ISTA), Fast Iterative Shrinkage-Thresholding (FISTA) and an accelerated Forward-Backward Nesterov type method. This study will be be carried out from a theoretical and computational point of view.
publishDate 2022
dc.date.accessioned.fl_str_mv 2022-10-18T13:04:16Z
dc.date.available.fl_str_mv 2022-10-18T13:04:16Z
dc.date.issued.fl_str_mv 2022-08-18
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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status_str publishedVersion
dc.identifier.citation.fl_str_mv RIBEIRO, D. N. Métodos de primeira ordem acelerados. 2022. 70 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/12377
dc.identifier.dark.fl_str_mv ark:/38995/0013000004v6m
identifier_str_mv RIBEIRO, D. N. Métodos de primeira ordem acelerados. 2022. 70 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.
ark:/38995/0013000004v6m
url http://repositorio.bc.ufg.br/tede/handle/tede/12377
dc.language.iso.fl_str_mv por
language por
dc.relation.program.fl_str_mv 70
dc.relation.confidence.fl_str_mv 500
500
500
500
dc.relation.department.fl_str_mv 27
dc.relation.cnpq.fl_str_mv 795
dc.relation.sponsorship.fl_str_mv 5
dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Goiás
dc.publisher.program.fl_str_mv Programa de Pós-graduação em Matemática (IME)
dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Matemática e Estatística - IME (RG)
publisher.none.fl_str_mv Universidade Federal de Goiás
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFG
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