Estudo de alguns metodos determinsticos de otimização irrestrita / Study of some deterministic methods for unconstrained optimization

AUTOR(ES)

Milena Almeida Leite Brandão

DATA DE PUBLICAÇÃO

2010

RESUMO

In this work some classical methods of linear search for unconstrained optimization are studied. The main mathematical formulations for the optimization problem are presented. Two strategies, linear search and trust region, for the algorithm to move from one iteration to another are discussed. Furthermore, the main considerations about the choice of step length along the search direction to ensure the convergence of the methods are exposed. Among the methods studied, some methods minimize a function of several variables without using derivatives (Cyclic Coordinates, Hooke and Jeeves with line searches and discrete steps and Rosenbrock). In the other methods the search direction is obtained by using derivatives of the objective function (Steepest Descent, Newton, Davidon-Fletcher-Powell, Broyden-Flotcher-Goldfarb-Shanno and Conjugate Gradient). For illustration, two optimization problems, one theoretical and one practical, are solved using the methods mentioned. The results are analyzed and comparisons between the studied methods are presented.

ASSUNTO(S)

otimização irrestrita line search methods metodos de busca linear matematica metodos classicos de otimização unconstrained optimization otimização matemática otimização determinstica deterministic optimization análise numérica classical methods of optimization

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