{"id":{"repo_id":"brazil-uerj","oai_identifier":"oai:pantheon.ufrj.br:11422/8174"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-uerj/oai:pantheon.ufrj.br:11422/8174","repository":{"repo_id":"brazil-uerj","name":"Brazil UERJ","base_url":"https://pantheon.ufrj.br/oai/request"},"display":{"title":"Método do ponto proximal inexato para minimização quase-convexa em variedades de Hadamard","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Cusihuallpa, Nancy Baygorrea"],"institution":"Universidade Federal do Rio de Janeiro","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Maculan Filho, Nelson"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-02","date_published":"2017-02","updated_at":"2026-07-24T01:16:29Z","subjects":["Engenharia de Sistemas e Computação","Método do ponto proximal","Variedades de Hadamard"],"languages":["por"],"rights":["Acesso Aberto"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11422/8174","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Maculan Filho, Nelson"]},{"key":"dc:creator","label":"Author","values":["Cusihuallpa, Nancy Baygorrea"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-05-23T17:51:56Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-16T03:05:41Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-02"]},{"key":"dc:publisher","label":"Institution","values":["Universidade Federal do Rio de Janeiro"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"]},{"key":"dc:type","label":"Dc Type","values":["Tese"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engenharia de Sistemas e Computação","Método do ponto proximal","Variedades de Hadamard"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["por"]},{"key":"dc:rights","label":"Dc Rights","values":["Acesso Aberto"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11422/8174"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Método do ponto proximal inexato para minimização quase-convexa em variedades de Hadamard"]}]}],"canonical_facts":{"dc:contributor.advisor":["Maculan Filho, Nelson"],"dc:creator":["Cusihuallpa, Nancy Baygorrea"],"dc:date.accessioned":["2019-05-23T17:51:56Z"],"dc:date.available":["2026-05-16T03:05:41Z"],"dc:date.issued":["2017-02"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11422/8174"],"dc:language":["por"],"dc:publisher":["Universidade Federal do Rio de Janeiro"],"dc:publisher.department":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"],"dc:rights":["Acesso Aberto"],"dc:subject":["Engenharia de Sistemas e Computação","Método do ponto proximal","Variedades de Hadamard"],"dc:title":["Método do ponto proximal inexato para minimização quase-convexa em variedades de Hadamard"],"dc:type":["Tese"]},"updated_at":"2026-07-24T01:16:29Z"}