4. Consider the optimization problem min xAx - bx, where A E R"X is a PSD matrix with xER"2 max (a) Find the optimizer x*. (b) Solving a linear system directly using Gaussian elimination takes O(n3) time, which may be wasteful if the matrix A is sparse. For this reason, we will use gradient descent to compute an approximation to the optimal point x*. Write down the update rule for gradient descent with a step size of 1. (c) Show that the iterates x(k) satisfy the recursion x(k)-X*-(J-A)(X(k-i)-r) (d) Using exercise 3 in Problem 3, prove |lAll2 S Amax(A)lll2. Hint: Use the fact that, if is an eigenvalue of A, then - is an eigenvalue of A2 (e) Using the previous two parts, show that for some 0