5. Consider the optimization problem: min: f1(x1) + f2(:L'2) + f3(1133) + 9(001 + 062 + 5173); where f1, f2, f3 and g are all convex functions of a single variable. In this exercise, we will get a better hint as to the potential benets of dual algorithms. (a) The lectures explained how to compute the dual of this problem, in the general case when the objective is of the form: f (as) + g(Aa3). In this case, f () has special structure: f(93) = f($17$27$3) = f1($1) + M902) + f3(963), and A as well has specied form. Using these, derive the dual optimization problem. It is a univariate optimization problem. (b) Now, write the dual update. As explained in the lecture, computing the update itself requires solving an optimization problem. Write down the update explicitly, and show that it can be computed by solving three univariate optimization problems