Notice that for small values of c, fc(u) = √ c2 + u2 ≈ |u|, or in words, fc(u)is a continuous approximation for the discontinuous function |u|. Consider using this approximation to solve the median...

Notice that for small values of c, fc(u) = √ c2 + u2 ≈ |u|, or in words, fc(u)is a continuous approximation for the discontinuous function |u|. Consider using this approximation to solve the median regression problem as

                         minb i f (yi − xT i b).

What optimization methods may work here? Will Newton methods work? Why or why not?