Hinge-loss optimality weight
= Hinge-loss optimality weight
{title2=$\lambda_i\in[0,1]$}
The subgradient of $\max\{0,1-a_ix\}$ is $-\lambda_i a_i$, with $\lambda_i=1$ below the margin, $\lambda_i=0$ beyond it and $\lambda_i\in[0,1]$ at equality. For quadratic regularization the one-dimensional optimality condition is $\alpha nx=\sum_i\lambda_i a_i$. The optimizer can be unique even if the weights at equality are not.