Detalhes bibliográficos
Ano de defesa: |
2017 |
Autor(a) principal: |
Silva, Gilson do Nascimento
 |
Orientador(a): |
Ferreira, Orizon Pereira
 |
Banca de defesa: |
Ferreira, Orizon Pereira
,
Karas, Elizabeth Wegner,
Silva, Paulo José da Silva e,
Melo, Jefferson Divino Gonçalves de,
Gonçalves, Max Leandro Nobre |
Tipo de documento: |
Tese
|
Tipo de acesso: |
Acesso aberto |
Idioma: |
eng |
Instituição de defesa: |
Universidade Federal de Goiás
|
Programa de Pós-Graduação: |
Programa de Pós-graduação em Matemática (IME)
|
Departamento: |
Instituto de Matemática e Estatística - IME (RG)
|
País: |
Brasil
|
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/6995
|
Resumo: |
We consider Newton’s method for solving a generalized equation of the form f(x) + F(x) 3 0, where f : Ω → Y is continuously differentiable, X and Y are Banach spaces, Ω ⊆ X is open and F : X ⇒ Y has nonempty closed graph. Assuming strong regularity of the equation and that the starting point satisfies Kantorovich’s conditions, we show that the method is quadratically convergent to a solution, which is unique in a suitable neighborhood of the starting point. In addition, a local convergence analysis of this method is presented. Moreover, using convex optimization techniques introduced by S. M. Robinson (Numer. Math., Vol. 19, 1972, pp. 341-347), we prove a robust convergence theorem for inexact Newton’s method for solving nonlinear inclusion problems in Banach space, i.e., when F(x) = −C and C is a closed convex set. Our analysis, which is based on Kantorovich’s majorant technique, enables us to obtain convergence results under Lipschitz, Smale’s and Nesterov-Nemirovskii’s self-concordant conditions. |