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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| 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 |
| 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. |
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