UNRESTRICTED ONE-DIMENSIONAL METHODS APPLIED TO SOLVING NON-LINEAR PROGRAMMING PROBLEMS

Authors

  • Simone Silva Frutuoso de Souza UNEMAT

DOI:

https://doi.org/10.36557/pbpc.v4i1.323

Keywords:

One-Dimensional Methods, Nonlinear Programming, Problem Solving

Abstract

This work aims to analyze unrestricted one-dimensional methods applied to solving nonlinear programming (NLP) problems. The methods involved will be: Golden section method, Bisection method and Newton's method. We use methods to solve a non-linear programming problem and analyze the performance of the three methods in an evaluative and comparative way. Issues such as number of iterations, execution time, optimal point found, will be part of analyzing good performance. Each method has a different methodology to solve the problem, so through analysis it is possible to verify how the problem is resolved and identify the best performance. To implement the methods used is the Matlab software. For the analysis, a classic non-linear problem presented in the bibliography will be used, in order to be able to visualize and verify the results obtained in the method simulations.

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References

BAZARAA, MOKHTAR S.; SHERALI, HANIF D.; SHETTY, C. M. Nonlinear programming: theory and algoritms, 2. Ed – Nova Iorque – Wiley – 1993.

BUZBY. B. R. Techniques and experience solving really big nonlinear programs, Optimization Methods, English Universities Press – London – 1974.

DAVIDON, W.C. Variance Algorithm for Minimization, Computer J – 406 – 410 – 1995.

GILAT, A; SUBRAMANIAM, V. Métodos numéricos para Engenheiros e Cientistas, Porto Alegre – Bookman – 2008.

JACOBY, S. L. S.; KOWALIK, J. S.; PIZZO, J. T. Iterative Methods for nonlinear optimization problems. Prentice-Hall – 1972.

LUENBERGER, D. G. Introduction to Linear and Nonlinear Programming, Addison – Wesley – 1984.

NERY, R. S. Métodos Híbridos para resolução de problemas de programação não linear, Universidade de São Paulo – USP – Monografia curso de matemática aplicada a negócios – 2007.

Published

2025-02-18

How to Cite

SILVA FRUTUOSO DE SOUZA, Simone. UNRESTRICTED ONE-DIMENSIONAL METHODS APPLIED TO SOLVING NON-LINEAR PROGRAMMING PROBLEMS. Periódicos Brasil. Pesquisa Científica, Macapá, Brasil, v. 4, n. 1, p. 2588–2606, 2025. DOI: 10.36557/pbpc.v4i1.323. Disponível em: https://periodicosbrasil.emnuvens.com.br/revista/article/view/323. Acesso em: 7 jun. 2025.

Issue

Section

Ciências Exatas e Engenharia