SVM dual optimization extra constraint

Question

In the svm notes at page 12, the author has presented the dual optimization problem. Why is there an extra constraint:

$$\sum_{i=0}^{m} \alpha_{i} y^{(i)}=0$$On reading up about the conversion of primal to dual, everywhere it shows only this constraint in the dual problem: $$\lambda_{i} \geq 0$$. The constraint $$\sum_{i=0}^{m} \alpha_{i} y^{(i)}=0$$ came up when we were differentiating $$L(w,b,\alpha)$$ wrt b and we used that constraint already in order to derive the final form of the $$L(w,b,\alpha)$$ without w and b in it.

Answer 1

While we have used that in the derivation of the objective function, this constraint still has to be satisfied.

Without imposing this constraint, our solver doesn't know that we have to satisfy this constraint hence the constraint is imposed.