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I have been studying SVM lately, following Andrew Ng's CS229 lecture notes. I can understand most of the notes. But for the case where the KKT condition is satisfied at alpha = C, I am not sure what that means.

I know that for alpha = 0, the KKT condition is satisfied with inequality constraint, namely, the point lies above the decision function yi * (w' * xi + b) = 1. And for 0 < alpha < C, the KKT condition is satisfied with equality constraint, namely, the point is a support vector. Now as for the case where alpha = C, I wonder what does this mean, does it mean that the point violate the constraint and that the penalty is C * slack_variable?

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$C$ is the maximum and $\alpha$ can be and indicates the Support Vector is inside the margin.

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