I want to find the dual of squared hinge objective. I know it must be similar to dual of $\text{SVM}$ formulation, wanted to double confirm how this will be calculated.
$$\min_{w,b}\sum_{i=1}^{M}[\max(0, 1-y_{i}(w^{T}x_{i}+b))]^{2}+\lambda||W||^{2}.$$
I went through Bishop and Deisenroth's book. These notes from Max welling are also helpful but all of them discuss linear cases. Here's where I'm stuck:
$\dfrac{1}{2}||w||^{2}-\sum_{i=1}^{M}2\alpha_{i}[y_{i}(w^{T}x_{i}+b)-1](y_{i}x_{i})$ such that $\alpha_{i}>0$. How to extract $w$ from here ?