1. no

    The minimization in the update rule is unaffected by $C$. Why are they there? Your explanation of it is not consistent with the update rule. You can also take the $\xi$ out of the argmin.

    • The minimization is subject to the second inequality. In my explanation xi=0, therefore L=0. When xi>0, the update rule has to find the minimum w(t+1) that satisfies the argmin (+ C*Xi) and L(w(t+1)) <= Xi.

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