Estudo de alguns métodos clássicos de otimização restrita não linear

• Ano de defesa: 2012
• Autor(a) principal: Oliveira, Fabiana Rodrigues de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Matemática; Ciências Exatas e da Terra; UFU
• Palavras-chave em Português: 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
• Link de acesso: https://repositorio.ufu.br/handle/123456789/16795; https://doi.org/10.14393/ufu.di.2012.65

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.