Apply GD and Newton algorithms to minimize the objective function (known as the Beale function) given by
 

Beale function) given by f(x) = (4xx - 4x+6) + (4xx 4x, +9)+(4xx 4x, +10.5) by doing the following: (a) Derive gradient and Hessian of the Beale function. (b) With each of the four initial points given below 2 -[3]. x = x 2 -=[3] -[] x(4) -3 and convergence tolerance & = 10-6, apply GD algorithm to minimize the Beale function. Report results in terms of (i) the solution point found, (ii) the value of the objective function at the solution point with an accuracy of at least 8 decimal places, and (iii) verify if the solution obtained is a local or global minimizer and explain why. (c) With the same initial points and convergence tolerance as in part (b), apply Newton algorithm to minimize the Beale function. Report results in terms of (i) the solution point found, (ii) the value of the objective function at the solution point with an accuracy of at least 8 decimal places, and (iii) verify if the solution obtained is a local or global minimizer and explain why. (d) Compare and comment the results obtained in parts (b) and (c).