# How are Lagrangian multipliers zero except for support vectors in dual representation of SVM?

How can we conclude that the Lagrangian multipliers are zero, except support vectors, in a dual problem? I cannot seem to see it.

$$L(\alpha)=-\frac{1}{2}\sum_i \sum_j \alpha_i \alpha_j y_i y_j x_i' x_j + \sum_i{\alpha_i}$$

Every constraint, $$g_i(x^*)\le 0$$ in the primal corresponds to a dual variable $$\mu_i$$ (Lagrange multiplier). The condition state that $$g_i(x^*)\mu_i=0$$
For points that are not support vectors, we have $$g_i(x^*)<0$$, hence we must have $$\mu_i=0$$.