With the notation of Exercise 21, for p = 2 the problem can be solved as in Example 9.15 using SVD. But it can also be solved using the techniques of constrained optimization:
(b) Form the KKT conditions of the resulting constrained optimization problem, obtaining a linear system of equations.
(c) Devise an example and solve it using the method just developed as well as the one from Example 9.15. Compare and discuss.
Example 9.15
(Minimum norm solutions of underdetermined systems). This case study is longer than usual and solves a problem which is a focus of current general interest.
Exercise 21
Consider the problem
Devise an example where solving with p = 2 actually makes more sense than with p = 1.