5:  Suppose we have sufficient training examples such that for each label pair (e t , e s ), there exists x i ∈ Gsatisfying e t ∈ R i ∪ {Θ}, e s ∈≺ (e t ).
the objective in Eq.6 becomes equivalent to max w j min 1≤s<t≤T +1 1 ||wt−ws|| and can be rewritten as min Moreover, to overcome the complexity brought in by the max operator, the objective of the optimization problem can be re-written by approximating the max operator with the sum operator.