Estudo de alguns métodos clássicos de otimização restrita não linear

In this work some classical methods for constrained nonlinear optimization are studied. The mathematical formulations for the optimization problem with equality and inequality constrained, convergence properties and algorithms are presented. Furthermore, optimality conditions of rst order (Karush-Ku...

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Detalles Bibliográficos
Autor: Oliveira, Fabiana Rodrigues de
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2012
País:Brasil
Institución:Universidade Federal de Uberlândia (UFU)
Repositorio:Repositório Institucional da UFU
Idioma:portugués
OAI Identifier:oai:repositorio.ufu.br:123456789/16795
Acceso en línea:https://repositorio.ufu.br/handle/123456789/16795
https://doi.org/10.14393/ufu.di.2012.65
Access Level:acceso abierto
Palabra clave:Otimização restrita
Programação não linear
Condições de Karush-Kuhn-Tucker
Simulação numérica
Convergência
Otimização matemática
Constrained optimization
Nonlinear programming
Karush-Kuhn-Tucker conditions
Numerical simulations
Convergence
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Descripción
Sumario:In this work some classical methods for constrained nonlinear optimization are studied. The mathematical formulations for the optimization problem with equality and inequality constrained, convergence properties and algorithms are presented. Furthermore, optimality conditions of rst order (Karush-Kuhn-Tucker conditions) and of second order. These conditions are essential for the demonstration of many results. Among the methods studied, some techniques transform the original problem into an unconstrained problem (Penalty Methods, Augmented Lagrange Multipliers Method). In others methods, the original problem is modeled as one or as a sequence of quadratic subproblems subject to linear constraints (Quadratic Programming Method, Sequential Quadratic Programming Method). In order to illustrate and compare the performance of the methods studied, two nonlinear optimization problems are considered: a bi-dimensional problem and a problem of mass minimization of a coil spring. The obtained results are analyzed and confronted with each other.