How are Lagrangian multipliers zero except for support vectors in dual representation of SVM?
In optimization, we have something called complementary slackness condition, it is part of the KKT conditions.

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 $g_i(x^*)&lt;0$, hence we must have $\mu_i=0$.