Um estudo do método de gradientes conjugados não lineares

Abstract

This work describes a study on iterative methods for solving the unconstrained minimization of smooth functions. More specifically, we address the steepest descent method, the linear conjugate gradient method and the nonlinear conjugate gradient method. A geometrical study of bidimensional problems is provided, illustrating distinct results as a consequence of the initial point, the demanded precision and the parameters that define the line search. Additionally, we have prepared a study involving four different expressions for the scalar in charge for maintaining the conjugacy of the directions. Although the results are equivalente in the linear case, there are significant differences in the nonlinear case, illustrated with several instances of the Broyden tridiagonal problem, with dimension from 2 up to 45.