7. Consider the least-norm problem min 12c /2 CERn subject to Ax = b 1. Introduce the Lagrange multipler A E R" to obtain the following un-constrained form of the problem: min 120 12 + AT ( Axc - 6) CERn 2. Show that Vu(x) = 2x + A'd 3. By setting the gradient to zero, and using Ax = b, show that at the minimizer - AA ) = b N and conclude the minimizer x = A (AAT ) -1b (provided AA is invertible). 4. In recent years, e -norm problems have become increasingly popular to obtain sparse solutions of Ax = b. Here, one minimizes the 1-norm of x subject to the constraint