Suggest effective methods for solving the penalized least squares problem               min(y − Xb) T (y − Xb) + λ(b − b∗) T A(b − b∗) for several values of λ at once. Formulate the p = ∞ norm...

Suggest effective methods for solving the penalized least squares problem

              min(y − Xb) T (y − Xb) + λ(b − b∗) T A(b − b∗)

for several values of λ at once.

Formulate the p = ∞ norm regression minb maxi |yi − xT i b| as a linear programming problem. Demonstrate the sensitivity of the resulting estimators to outliers.