solve Part C only

2. In the gradient descent (2), for distance between a and a"), we used the 2-norm, which can be replaced by other norms to obtain variants of the gradient descent algorithm. (a) Prove that (2) is equivalent to x( *+1) = arg min (Vf(a(*) ), x - x)), subject to la - 2|2 Sox|Vf(a(*)) |2. (3) CER" (Hint: Use Cauchy-Schwartz inequality.) (b) We may replace the 2-norm in (3) by 1-norm, i.e., x(*+1) = arg min (Vf(a(*) ), x - 2*), subject to |x - x)|1 5 axlVf(a(*))|x. (4) Give an explicit expression of a(*+1) in (4). (Hint: Use the inequality (x, y) |