Consider the Freudenstein and Roth test function F(x) = f_1(x)^2 + f_2(x)^2, x element R^2, where f_1(x) = -13 + x_1 + ((5 - x_2)x_2 - 2)x_2, f_2(x) = -29 + x_1 + ((x_2 + 1)x_2 - 14)x_2 Show that the function f has three stationary points. Find them and prove that one is a global minimizer, one is a strict local minimum and the third is a saddle point. Use LAB to employ the following three methods on the problem of minimizing f the gradient method with backtracking and parameters (s, alpha, beta) = (1, 0.5, 0.5) the hybrid Newton's method with parameters (s, alpha, beta) = (0.5, 0.5) damped Gauss-Newton's method with a backtracking line search strategy with parameters (s, alpha, beta) = (1, 0.5, 0.5) All the algorithms should use the stopping criteria ||nebla f (x)|| lessthanorequalto 10^-5. Each algorithm should be employed four times on the following four starting points: (-50, 7)^T (20, 7)^T 20, -18)^T, (5, -10)^T. For each of the four start ing points, compare the number of iterations and the point to which each method converged. If a method did not converge, explain why. Consider the Freudenstein and Roth test function F(x) = f_1(x)^2 + f_2(x)^2, x element R^2, where f_1(x) = -13 + x_1 + ((5 - x_2)x_2 - 2)x_2, f_2(x) = -29 + x_1 + ((x_2 + 1)x_2 - 14)x_2 Show that the function f has three stationary points. Find them and prove that one is a global minimizer, one is a strict local minimum and the third is a saddle point. Use LAB to employ the following three methods on the problem of minimizing f the gradient method with backtracking and parameters (s, alpha, beta) = (1, 0.5, 0.5) the hybrid Newton's method with parameters (s, alpha, beta) = (0.5, 0.5) damped Gauss-Newton's method with a backtracking line search strategy with parameters (s, alpha, beta) = (1, 0.5, 0.5) All the algorithms should use the stopping criteria ||nebla f (x)|| lessthanorequalto 10^-5. Each algorithm should be employed four times on the following four starting points: (-50, 7)^T (20, 7)^T 20, -18)^T, (5, -10)^T. For each of the four start ing points, compare the number of iterations and the point to which each method converged. If a method did not converge, explain why