I have the following convex optimization problem: \begin{equation}\label{prob} \begin{aligned} &\underset{{\bf W, \xi}}{\text{min}} & \frac{1}{2} ||{\bf W}||_2^2 + \sum_{i=1}^n C_{y_i}\max(0,1+ \underset{r \neq y_i}{\max} {\bf W}_{r}^T {\bf x}_i - {\bf W}_{y_i}^T {\bf x}_i )) \\ & \text{subject to} & \forall i, \forall r \neq y_i, \quad {\bf W}_{y_i}^T {\bf x}_i- {\bf W}_{r}^T {\bf x}_i + \xi_i \geq 1\\ & &\forall i, \xi_i \geq 0 \end{aligned} \end{equation}
where ${\bf W}$ is a matrix of size $\mathbb{R}^{K \times d}, {\bf x}_i \in \mathbb{R}^{1 \times d}, y_i \in \{1,2,...,K\} $, $K$ is the number of classes. The matrix ${\bf W}$ stores weight vector for each class in its rows. $C_{y_i} = C / N_{y_i}$ is the regularization parameter weighted inversely by the number of data points in that class. ${\bf W}_{j}$ denotes the row of ${\bf W}$ corresponding to label/class $j$.
How can I convert this constrained problem into unconstrained?