If this is the constrained version of ridge regression:
min w∈Rd ∥Φw − y∥^2 s.t. ∥w∥2 ≤ s, (1)
where Φ ∈ R n×d and y ∈ R n . Answer the following questions.
•How can we prove that this is a convex optimization problem.
•Does strong duality really hold? If yes, derive the KKT condition regarding the optimal solution w∗ for the above problem.
• Does a closed-form solution exist? If yes, derive the closed-form solution. If not, can you propose an algorithm for computing the optimal solution (describe the key steps of your algorithm)? Please Help