Programa de Pós-graduação em Matemática
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Navegando Programa de Pós-graduação em Matemática por Por Orientador "FERREIRA, Orizon Pereira"
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Item Método do gradiente para funções convexas generalizadas(Universidade Federal de Goiás, 2009-12-16) COUTO, Kelvin Rodrigues; FERREIRA, Orizon Pereira; lattes.cnpq.br/0201145506453251The Convergence theory of gradient method and gradient projection method, for minimization of continuously differentiable generalized convex functions, that is, pseudoconvex functions and quasiconvex functions is studied in this work. We shall see that under certain conditions the gradient method, as well as gradient projection method, generate a convergent sequence and the limit point is a minimizing, whenever the function has minimizing and is pseudoconvex functions. If the objective function is quasiconvex then the generated sequence converges to a stationary point whenever that point exists.Item Convergência local do método de Newton inexato e suas variações do ponto de vista do princípio majorante de kantorovich(Universidade Federal de Goiás, 2007-12-14) GONAÇALVES, Max Leandro Nobre; FERREIRA, Orizon Pereira; lattes.cnpq.br/0201145506453251The search for solutions of nonlinear equations in the Euclidean spaces is object of interest in some areas of science and engineerings. Due the speed of convergence and computational efficiency, the inexact Newton method and its variations have been suficiently used to obtain solutions of these equations. In this dissertation we present a local analysis of convergence of the inexact Newton method and some of its variations, more specifically the inexact Newton-like method and the inexact modified Newton method. This analysis has the disadvantage to demand the previous knowledge of a zero of the operator in consideration and the hypotheses on the behavior of the operator at this zero, but on the other hand it supplies to information on the convergence rate and convergence radius.Item Problemas de Otimização Quase Convexos: Método do Gradiente para Funções Escalares e Vetoriais(Universidade Federal de Goiás, 2011-10-27) SANTOS, Milton Gabriel Garcia dos; FERREIRA, Orizon Pereira; lattes.cnpq.br/0201145506453251This work we study the convergence properties of the Gradient Method Designed and Descent Method for Multi-objective optimization. At first, our optimization problem is to minimize a real function of n-variables, continuously differentiable and restricted to a set of simple structure and add on the objective function of the hypothesis of pseudo-convexity or quasi-convexity. Then we consider the problem of unconstrained multi-objective optimization and add some hypotheses about the function vector, such as convexity or quasi-convexity, and is continuously differentiable. It is noteworthy that in both problems will be used to search for inexact Armijo over viable directions.