Artigo Completo - Open Access.

# SOME CLASSICAL OPTIMIZATION METHODS

### Silva, Pedro Henrique Rodrigues da ; Brandão, Milena Almeida Leite ;

##### Artigo Completo:

In general terms, optimizing means to plan or develop more efficiently. After the formulation of the model, an optimization method is used to obtain the solution of the problem. We can divide the optimization methods among those dependent or not the knowledge derived. The optimization methods that do not depend on the use of derivatives generally using only information of the function to be optimized, which may be discontinuous and multimodal. The major advantage of these methods is the great practical potential due to the increasing need to solve optimization problems defined by functions for which there are no derived or these are available at a very high computational cost. In optimization methods that dependent upon use of derivatives the model is completely known and are for continuous, convex and semi-modal functions. In this study, two optimization methods are presented: the Method of Cyclic Coordinates, which does not depend on derivatives it uses the direction of the coordinate axes as search directions and the Newton Method whose search direction using the derivatives of the function to be optimized. Then a mathematical modeling problem will be solved by both methods and the results will be analyzed.

Palavras-chave: Otimização Determinística, Método das Coordenadas Cíclicas, Método de Newton, Deterministic Optimization, Method of Cyclic Coordinates, Newton’s Method,

Palavras-chave: ,

DOI: 10.5151/mathpro-cnmai-0068

##### Referências bibliográficas
• [1] Bazaraa, S.M., Sherali, H.D, Shetty, C.M., 2006. Nonlinear Programming Theory and Algorithms, 3rd ed., John Wiley Andamp; Sons, Atlanta.
• [2] Brand˜ao, M. A. L. 2010. Estudo de alguns métodos determinísticos de otimização irrestrita Dissertação de Mestrado, Universidade Federal de Uberlândia, (pp 101). Uberlândia, Brasil.
• [3] Camponogara, E. 2006. Métodos de otimização: Teória e Prática Universidade Federal de Santa Catarina, Departamento de Automação e Sistemas, Florianópolis, Brasil.
• [4] Dasgupta, D., Le Riche, R., Michalewicz, Z. e Schönhauer, M. 1996. Evolutionary Algorithms for Constrained Engineering Problems Computers e Industrial Engineering Journal
• [5] Hartman, H. L. ; Mutmansky, J. M. 2002. Introductory Mining Engineering New Jersey: John Wiley e Sons, second edition.
• [6] Nocedal, J., Wright, S.J. 2000. Numerical Optimization, Springer Series in Operations Research
• [7] Stewart, J. 200 Cálculo, Vol. 2. 5ed. São Paulo: Thomson Learning
• [8] Takahashi, R. 2003. Otimização Escalar e Vetorial Universidade Federal de Minas Gerais, Departamento de Matemática, Curso de Verão.
##### Como citar:

Silva, Pedro Henrique Rodrigues da; Brandão, Milena Almeida Leite; "ALGUMS MÉTODOS CLÁSSICOS DE OTIMIZAÇÃO", p. 384-392 . In: Anais do Congresso Nacional de Matemática Aplicada à Indústria [= Blucher Mathematical Proceedings, v.1, n.1]. São Paulo: Blucher, 2015.
ISSN em b-reve, DOI 10.5151/mathpro-cnmai-0068

últimos 30 dias | último ano | desde a publicação