I recently came across a statement that the unconstrained primal L2-regularized SVM formulation $$ \min_\mathbf{w} \lambda \|\mathbf{w}\|^2_2 + \sum_i \max (0, \; 1 - y_i \mathbf{w}^T\mathbf{x}_i) $$ is equivalent to a primal constrained formulation \begin{align} \min_\mathbf{w} \sum_i \max (0, \; 1 - y_i \mathbf{w}^T\mathbf{x}_i) \\ \text{s.t.} \qquad \|\mathbf{w}\|_2 \le \frac{1}{\sqrt{\lambda}} \end{align}
I found no traces of it in the internet, and I can't see what's the intuition behind and the proof of it. Any ideas? Thx.