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Ricardo Hiroshi Caldeira Takahashihttp://lattes.cnpq.br/4947186824317781Renato Cardoso MesquitaAlexandre Salles da CunhaAlexandre Cláudio Botazzo DelbemEduardo Camponogarahttp://lattes.cnpq.br/2751159050825277Ivo Fagundes David de Oliveira2022-04-28T19:42:51Z2022-04-28T19:42:51Z2021-12-06http://hdl.handle.net/1843/41216https://orcid.org/0000-0001-8450-5054This thesis presents a series of improvements on four different classical searching methods employed for solving different well established problems. The methods improved on and their corresponding problems are: (i) the bisection method for continuous root-searching problems; (ii) the binary search algorithm for discrete list-searching; (iii) the back-tracking technique for inexact Armijo-type searching; and (iv) the n-dimensional steepest descent method for non-linear multi-objective optimization. Different types of improvements are aimed for in each context that produce an overall reduction in the the number of calls to the external function being searched. However, all four improvements proposed have one thing in common: the worst-case upper-bound of our methods either outperform the state-of-the-art, or, where the state-of-the-art has already attained an optimal worst-case performance, we match the performance of the optimal bound while improving on either average performance, asymptotic performance or both. Thus, in this sense, the methods we propose are \emph{strict} improvements on classical solutions, attained with no additional assumptions on the problems considered nor with any additional costs other than the computation of the methods themselves. The manuscript starts with a broad introduction which discusses the importance of the problems considered and the classical solutions employed in several different fields. The main contributions are given in the following four chapters; one corresponding to each problem tackled. Each chapter corresponds to one published (or soon to be published) result intimately related to the four problems considered which are augmented with original unpublished material. Finally, in the sixth and final chapter we point to possible ramifications of the findings hereby delineated which present potential for future developments.Esta tese apresenta uma série de melhorias em quatro métodos clássicos de busca empregados para resolver quatro problemas bem estabelecidos. Os métodos aprimorados e seus problemas correspondentes são: (i) o método da bissecção para problemas de busca de raízes; (ii) o algoritmo de busca binária para procura em listas discretas; (iii) a técnica de back-tracking para buscas inexatas do tipo Armijo; e (iv) o método de otimização utilizando a direção de maior descida para problemas multi-objetivo. Diferentes tipos de melhorias são produzidas em cada instância que, de forma geral, produzem uma redução no número de chamadas à função externa que está sendo procurada. No entanto, todas as quatro melhorias propostas têm uma coisa em comum: as garantias de pior caso dos nossos métodos sempre apresentam uma melhoria em relação ao estado da arte e, quando o estado da arte já apresenta um desempenho de pior caso ótimo, então, os nossos métodos apresentam um desempenho médio ou desempenho assintótico aprimorados em relação ao estado da arte. Neste sentido, os métodos que propomos são melhorias estritas sobre as soluções clássicas, obtidas sem suposições adicionais sobre os problemas considerados e nem com custos adicionais escondidos. O manuscrito começa com uma ampla introdução que discute a importância dos problemas considerados e as soluções clássicas empregadas em vários campos diferentes. As principais contribuições são dadas no quatro capítulos subsequentes. Cada capítulo corresponde a uma resultado publicado (ou em vias de ser publicado) com a adição de material exclusivo à tese intimamente relacionados com os quatro problemas considerados. No sexto e último capítulo, apontamos as possíveis ramificações das descobertas aqui delineadas, que apresentam potencial para desenvolvimentos futuros.engUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em Engenharia ElétricaUFMGBrasilENG - DEPARTAMENTO DE ENGENHARIA ELÉTRICAhttp://creativecommons.org/licenses/by/3.0/pt/info:eu-repo/semantics/openAccessEngenharia elétricaOtimização matemáticaOtimização multiobjetivoBinary searchingRoot searchingLine searchingList searchingGradient methodMultiobjective optimizationBacktrackingLimits and improvements on searching and optimization: from one dimensional problems to multi-objective optimizationLimites e aprimoramentos em busca e otimização: de problemas unidimensionais até otimização multi-objetivoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALTeseDoutoradoIvo_Editado2.pdfTeseDoutoradoIvo_Editado2.pdfapplication/pdf10061597https://repositorio.ufmg.br/bitstream/1843/41216/6/TeseDoutoradoIvo_Editado2.pdff3a6f5fb281bf190972f7868e6ed7162MD56CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufmg.br/bitstream/1843/41216/2/license_rdff9944a358a0c32770bd9bed185bb5395MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/41216/7/license.txtcda590c95a0b51b4d15f60c9642ca272MD571843/412162022-04-28 16:42:52.148oai:repositorio.ufmg.br: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ório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2022-04-28T19:42:52Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
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