Substituting, we have except the constraint that µ = −c − λ implies that for µ to be positive λ ≤ c. Since this Lagrangian has the same form as equation 3, we can also derive a dual problem, which is the same as in equation 4, with the additional constraint that each λ i can not be bigger than its cost c i .
the dual problem can not penalize the violation of a constraint more than the soft constraint model in the primal would penalize you if you violated it.