We have the following primal problem
$$\min_{ \mathbb W_{i,j} \in \mathbb R, \, \xi_{i,j} \in \mathbb R, \, b \in \mathbb R^m} - \sum\limits_{i=1}^{n} \sum\limits_{j=1}^{m} \xi_{i,j} + \frac{1}{2} \sum\limits_{i=1}^{l} \mathbb W_{i}^2$$
such that
$$\mathbb W_i x_i + b_{y_i} - \mathbb W_j x_i - b_j \geq 1 - \xi_{i,j}$$
$$\xi_{i,j} \geq 0$$
$$\xi_{i:y_i=j,j} = 1$$
for $i=1, \dots, n$, $j=1, \dots, m $
$\mathbb W_i$ denotes the i-th row of the matrix $\mathbb W$, $x_i$ is a vector of length compatible with $\mathbb W$ and $\xi_{i:y_i=j,j} = 1$ means that we fix this $\xi_{i,j}$ to 1 if $y_i=j$
Any idea how to write the Lagrangian and then the dual this problem ?