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

This paper aims to perform a comprehensive analysis of unconstrained one-dimensional methods, focusing on their application in solving nonlinear programming (NLP) problems. Three optimization methods will be explored: the Golden Section method, the Bisection method and the Newton method. In order to evaluate and compare the performance of each method, they will be applied to solving an NLP problem. The analysis will be carried out based on parameters such as the number of iterations required for convergence, execution time, the optimal point found and the accuracy of the solution. Each method has a distinct methodology to approach the optimization problem. Through comparative analysis, it will be possible to understand how each method operates and identify its advantages and disadvantages in relation to the others. The implementation of the methods will be carried out using MATLAB software, widely used in numerical calculations and simulations. To guarantee the reliability of the analysis, a classic non-linear problem will be used, present in the bibliography consulted. This approach will make it possible to visualize and prove the results obtained in the simulations, validating the comparative analysis of the methods. It is expected that this work will contribute to the understanding of unrestricted one-dimensional methods and their applications in NLP problems, providing relevant information for choosing the most appropriate method for each situation.