Método do ponto proximal inexato para minimização quase-convexa em variedades de Hadamard

• Ano de defesa: 2017
• Autor(a) principal: Cusihuallpa, Nancy Baygorrea
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Rio de Janeiro; Brasil; Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia; Programa de Pós-Graduação em Engenharia de Sistemas e Computação; UFRJ
• Palavras-chave em Português: Engenharia de Sistemas e Computação; Método do ponto proximal; Variedades de Hadamard; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO
• Link de acesso: http://hdl.handle.net/11422/8174

In this thesis, we present an inexact proximal point algorithm to solve quasiconvex optimization problems in Riemannian manifolds with non positive sectional curvature, called Hadamard manifolds. Then, we show that under mild hypotheses on the optimization problem, the sequence generated by the proposed method are well defined and converge to critical points of the problem. We also prove that the convergence rate of the ones is linear and superlinear in some cases. Furthermore, by focusing on the importance of applications in economics and localization theory, we extend the proposed algorithm for solving multiobjective quasiconvex optimization problem. Moreover, convergencia of the sequence to a Pareto-Clarke critical point is obtained assuming reasonable hypotheses. Finally, computational experiments were done to validate the proposed model and results found.