Consider the problem minimize f(x) = 1 2 x2 1 + |x2| + 2x2 subject to x2 = 0, where > 1. (a) Calculate the optimal solution and the Lagrange multiplier. (b) Write a computer program to calculate the iterates of the multiplier method with 0 = 0, and ck = 1 for all k. Confirm computationally that the rate of convergence is sublinear if = 1.5, linear if = 2, and superlinear if = 3. (c) Give a heuristic argument why the rate of convergence is sublinear if < 2, linear if = 2, and superlinear if > 2. What happens in the limit where = 1