How do we find the parameter b and the vector \boldsymbol{w} ? What we could do is to define a cost function which now contains the set of all misclassified points M and attempt to minimize this function C(\boldsymbol{w},b) = -\sum_{i\in M} y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b).
We could now for example define all values y_i =1 as misclassified in case we have \boldsymbol{w}^T\boldsymbol{x}_i+b < 0 and the opposite if we have y_i=-1 . Taking the derivatives gives us \frac{\partial C}{\partial b} = -\sum_{i\in M} y_i, and \frac{\partial C}{\partial \boldsymbol{w}} = -\sum_{i\in M} y_ix_i.