Line search in descent methods

In this thesis, we deal with descent methods for functional minimalization. We discuss three conditions for the choice of the step length (Armijo, Goldstein, and Wolfe condition) and four descent methods (The steepest descent method, Newton's method, Quasi-Newton's method BFGS and the conjugate gradient method). We discuss their convergence properties and their advantages and dis- advantages. Finally, we test these methods numerically in the GNU Octave pro- gramming system on three different functions with different number of variables.