The object of this thesis is to study the multi-criteria linear fractional programming problems (MLFP). The characterizations of efficiency, weak efficiency and proper efficiency are derived. In the bicriteria case, the set E of all efficient solutions of (MLFP) is path-connected by a finite number of line segments and the efficient frontier F(E) can be evaluated by using the row parametric technique in linear programming. The weakly efficient (respectively, properly efficient) solutions can be generated by solving the generalized Tchebycheff norm problems (Tβ) (respectively, (βα)) with different parameters β and α. The set E[sup=W] of all weakly efficient solutions of (MLFP) is compact and path-connected by finitely many line segments. A dual problem is formulated which is a natural extension of the usual dual in linear programming, the Wolfe dual in nonlinear programming and the Isermann dual in multiple objective linear programming. Duality results are established under the assumption that the criteria are concave functions. The matrix of the dual variables of (MLFP) can be evaluated by solving L linear programs. A heuristic arrow search algorithm is developed for solving general multicriteria programming problems interactively. The decision maker merely selects his most preferred one amongst-the presented alternatives. Solutions generated are evenly distributed over the desired neighbourhood of the weakly efficient frontier. The algorithm is convergent in the bicriteria case, with appropriate convexity conditions. When applied to solve (MLFP), the arrow search algorithm uses only the linear programming techniques. / Business, Sauder School of / Graduate

Orientador: Antonio Carlos Moretti / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-07-23T19:43:21Z (GMT). No. of bitstreams: 1 Feitosa_AndreaHamazaki_M.pdf: 707160 bytes, checksum: b236f7713a538bf3a8276ef5239cf979 (MD5) Previous issue date: 1998 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática Aplicada

Orientador: Hermano de Medeiros Ferreira Tavares / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Campinas / Made available in DSpace on 2018-07-19T03:52:18Z (GMT). No. of bitstreams: 1 Arenales_MarcosNereu_D.pdf: 1849471 bytes, checksum: 178e68ebf5014f1ff779237f26098eea (MD5) Previous issue date: 1984 / Resumo: Não informado. / Abstract: Not informed. / Doutorado / Doutor em Engenharia Elétrica

Orientador: Marcos Vieira Teixeira / Resumo: A presente investigação teve como objetivo conceber uma cronologia histórica das primeiras noções de independência linear e de base de um espaço vetorial. Um recorte histórico com dezesseis autores, entre matemáticos e físicos, foi delineado. Dois artigos foram motivadores dessa pesquisa: The History of the Concept of a Finite-Dimensional Vector de Jeremy Gray (1980), que questionava o conceito e origem do espaço vetorial, estimulando um estudo mais aprofundado sobre o tema e The Axiomatization of Linear Algebra de Gregory Moore (1995) num trabalho sobre a axiomatização da Álgebra Linear entre 1875 a 1940. Foi elaborada extensa pesquisa em obras originais dos principais matemáticos do século XVII até o século XIX, considerando o relacionamento entre eles, troca de cartas e a conformidade de estudos. Essa busca foi efetuada nas principais bibliotecas digitais como Gallica, E rara, além sites especializados como Euler Archive, à procura de artigos e livros onde se apresentasse elementos que direcionassem para ideias de conjuntos linearmente independente e de base. De Leibniz a Peano, obras originais desses dezesseis matemáticos e físicos foram analisadas, trazendo essas ideias de conjuntos linearmente independentes e de base em diferentes contextos de áreas da Matemática e da Física. Iniciando com Leibniz, que percebeu a necessidade de um ente que representasse magnitude, direção e sentido, essa cronologia passou por Euler e Lagrange com a resolução de equações diferenciais, co... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The present investigation aimed to conceive a historical chronology of the first notions of linear and basic independence of a vector space. A historical section with sixteen authors, between mathematicians and physicists, was designed. Two articles motivated this research: The History of the Concept of a Finite-Dimensional Vector by Jeremy Gray (1980), which questioned the concept and origin of the vector space, stimulating a deeper study on the theme and The Axiomatization of Linear Algebra by Gregory Moore (1995) in a work on the axiomatization of Linear Algebra between 1875 and 1940. Extensive research was carried out on original works by leading mathematicians from the 17th to the 19th century, considering the relationship between them, exchange of letters and the conformity of studies . This search was carried out in the main digital libraries such as Gallica, E rara, in addition to specialized sites such as Euler Archive, looking for articles and books where elements were presented that would lead to ideas of linearly independent and basic sets. From Leibniz to Peano, original works of these sixteen mathematicians and physicists were analyzed, bringing these ideas from linearly independent and basic sets in different contexts in the areas of Mathematics and Physics. Starting with Leibniz, who realized the need for an entity that represented magnitude, direction and sense, this chronology went through Euler and Lagrange with the resolution of differential equations, Wes... (Complete abstract click electronic access below) / Doutor

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Orientador: Jose Mario Martinez / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-16T15:26:50Z (GMT). No. of bitstreams: 1 Santos_RitaFilomenaAlvesdos_M.pdf: 978640 bytes, checksum: 2e2df1568dc14b0909895f5db851f895 (MD5) Previous issue date: 1989 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática Aplicada

Submitted by JULIANA MALLIA ZACHI null (juzachi@yahoo.com.br) on 2016-09-28T00:44:55Z No. of bitstreams: 1 dissertacao.pdf: 6894521 bytes, checksum: f75c53a8798712cd2028eda75d209e76 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-09-28T14:35:50Z (GMT) No. of bitstreams: 1 zachi_jm_me_rcla.pdf: 6894521 bytes, checksum: f75c53a8798712cd2028eda75d209e76 (MD5) / Made available in DSpace on 2016-09-28T14:35:50Z (GMT). No. of bitstreams: 1 zachi_jm_me_rcla.pdf: 6894521 bytes, checksum: f75c53a8798712cd2028eda75d209e76 (MD5) Previous issue date: 2016-09-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho são apresentados os fundamentos da Programação Linear, em especial, da Programação Linear Geométrica, instrumento importante de otimização para problemas de Economia, gestão de empresas, problemas de transportes, obtenção de misturas ótimas, entre outros. Além disso, é apresentada uma proposta didática para os professores de educação básica da escola pública, utilizando o software GeoGebra como instrumento motivador para o estudo de uma situação de aprendizagem proposta no material de apoio idealizado pela Secretaria da Educação do Estado de São Paulo, abordada no caderno do aluno do 3º ano do Ensino Médio. / In this work presents the fundamentals of linear programming in particular, of geometric linear programming, important instrument of optimization for economic problems, business management, transport problems, obtaining optimal mixtures, among others. In addition, presents a didactic proposal for teachers of the basic education of public school, using the GeoGebra software as a motivating tool for the study of a learning situation proposed in the support material designed by the Education secretary of the State of São Paulo is presented, adressed in the student notebook of 3rd year of high school.