I'm trying to derive the dual form for the L2 support vector machine. I thought the Lagrangian should be of the form:
$L_p(w, b, \xi, \alpha) = \frac{1}{2} \| w \|^2 + \frac{C}{2} \sum_{i=1}^m \xi_i^2 - \sum_{i=1}^m \alpha_i \left( y_i (x_i \cdot w + b) - 1 + \xi_i \right) + \sum_{i=1}^m \mu \xi_i$
because of the constraint that $\xi_i \geq 0$.
However, looking online, I found that someone has written the Lagrangian as: $L_p(w, b, \xi, \alpha) = \frac{1}{2} \| w \|^2 + \frac{C}{2} \sum_{i=1}^m \xi_i^2 - \sum_{i=1}^m \alpha_i \left( y_i (x_i \cdot w + b) - 1 + \xi_i \right)$
I don't understand why the term $\sum_{i=1}^m \mu \xi_i$ can be omitted in the Lagrangian. Could someone help me understand this? Thank you!