Mestrado em Matemática (IME)
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Navegando Mestrado em Matemática (IME) por Por Orientador "Ferreira, Orizon Pereira"
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Item Unificando o análise local do método de Newton em variedades Riemannianas(Universidade Federal de Goiás, 2017-03-08) Guevara, Stefan Alberto Gómez; Ferreira, Orizon Pereira; http://lattes.cnpq.br/0201145506453251; Ferreira, Orizon Pereira; Gonçalves, Max Leandro Nobre; Santos, Paulo Sergio Marques dosIn this work we consider the problem of finding a singularity of a field of differentiable vectors X on a Riemannian manifold. We present a local analysis of the convergence of Newton's method to find a singularity of field X on an increasing condition. The analysis shows a relationship between the major function and the vector field X. We also present a semi-local Kantorovich type analysis in the Riemannian context under a major condition. The two results allow to unify some previously unrelated results.Item Método de Newton para encontrar zeros de uma classe especial de funções semi-suaves(Universidade Federal de Goiás, 2016-03-04) Louzeiro, Mauricio Silva; Ferreira, Orizon Pereira; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4785356U8; Ferreira, Orizon Pereira; Cruz, José Yunier Bello; Ribeiro, Ademir Alves; Prudente, Leandro da FonsecaIn this work, we will study a new strategy to minimize a convex function on a simplicial cone. This method consists in to obtain the solution of a minimization problem through the root of a semi-smooth equation associated to its optimality conditions. To nd this root, we use the semi-smooth version of the Newton's method, where the derivative of the function that de nes the semi-smooth equation is replaced by a convenient Clarke subgradient. For the case that the function is quadratic, we will see that it allows us to have weaker conditions for the convergence of the sequence generated by the semi-smooth Newton's method. Motivated by this new minimization strategy we will also use the semi-smooth Newton's method to nd roots of two special semi-smooth equations, one associated to x+ and the another one associated to jxj.Item Quadratic programming on the positive orthant with a quasiconvex objective function(Universidade Federal de Goiás, 2019-07-31) Zuñiga, Ruby Yohana Cuero; Ferreira, Orizon Pereira; http://lattes.cnpq.br/0201145506453251; Ferreira, Orizon Pereira; Gonçalves, Jefferson Divino; Prudente, Leandro da Fonseca; Sandoval, Wilfredo SosaIn this work, we will study a class of real symmetric matrices that we will call subdefinite, these matrices include the positive semidefinites. For our purpose we will focus on the merely positive subdefinite matrices, that is, those matrices that are positive subdefinite but are not positive semidefinite. We will discuss the quadratic functions on Rn + and show that these functions are quasiconvex not convex, when their matrix representation is given by a merely positive subdefinite matrix. In addition, we will present a result of great importance in quadratic programming given that it allows to reduce the quasiconvexity of these nonconvex quadratic functions to the pseudoconvexity in the semipositive orthant. Finally, we will study the conditional gradient method to solve the quadratic programming problem, where the objective function is of this type.