On each round of constraint induction the cutting-plane algorithm computes the arg max in Equation 6 for a training instance, which is referred to as loss-augmented prediction, and adds the corresponding constraint to the active set.
the constraints from Equation (5) are equivalent to: if loss-augmented prediction turns up no new constraints on a given iteration, the current solution to the reduced problem,ŵ andξ, is the solution to the full SVM training problem.