1: Gradient and Newton methods Consider the unconstrained problem min xR n f (x) = m j=1 log(1 a j x) n i=1 log(1 x 2 i ). Use initial point x (0) = 0 R n and generate instances of this problem by setting aj R n to be rand(n,1), where j = 1, . . . , m. You are free to pick any reasonable values for m and n (i.e., don't use m = n = 1). (a) Use the gradient method to solve the problem, using reasonable choices for the back- tracking parameters, and a stopping criterion of the form f (x) 2 . Plot the objective function and step length versus iteration number. Once you have determined the optimal value of the problem J with a high accuracy, you can also plot f J versus iteration number. Experiment with the backtracking parameters and to see their effect on the total number of iterations required. Carry these experiments out for several instances of the problem of different sizes. Hint 1 : Use the chain rule to find expressions for f (x) and 2 f