Problem 1 (20 points) Consider the problem minimize f(:c) = %mTQa: 6T3: EER\" with 1 0 0 1 Q = 0 *7 0 and b = 1 O 0 '72 1 Consider solving the problem using the steepest descent method (with exact line search). (a) (5 points) Suppose that you solve (DO NOT ACTUALLY SOLVE) the problem repeatedly for each value 7 = 1, '7 = 2, ..., 'y = 100. As the values of 7 get larger do you expect the convergence to be faster or slower? Explain your answer. (b) (15 points) For the problem instance with 'y = 2 compute the rst four iterations (i.e. compute up to and including (17(4)) of the steepest descent method with the initial point 113(0) 2 (O, 0, 0)T. Show all work for each iteration. For this problem, solve all optimization subproblems (Le. exact step lengths) by hand