Detalhes bibliográficos
Ano de defesa: |
2022 |
Autor(a) principal: |
Ribeiro, Douglas Nascimento
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Orientador(a): |
Melo, Jefferson Divino Gonçalves de
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Banca de defesa: |
Melo, Jefferson Divino Gonçalves de,
Alves, Maicon Marques,
Gonçalves, Max Leandro Nobre,
Ferreira, Orizon Pereira |
Tipo de documento: |
Dissertação
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Tipo de acesso: |
Acesso aberto |
Idioma: |
por |
Instituição de defesa: |
Universidade Federal de Goiás
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Programa de Pós-Graduação: |
Programa de Pós-graduação em Matemática (IME)
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Departamento: |
Instituto de Matemática e Estatística - IME (RG)
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País: |
Brasil
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Palavras-chave em Português: |
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Palavras-chave em Inglês: |
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Área do conhecimento CNPq: |
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Link de acesso: |
http://repositorio.bc.ufg.br/tede/handle/tede/12377
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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. |