SVM - Why Lagrange multiplier alpha must be smaller than or equal to C?

by FailedMathematician   Last Updated August 10, 2018 11:19 AM

According to this note page 20, SVM with slack $$0 \leq \alpha_i \leq C $$

Why is $\alpha_i \leq C $ and I don't understand how to arrive at equation 15 (I understand the meaning of those equations but I don't understand how to get to those equations ) on the same page: $$\alpha_i = C \Rightarrow y_i(w^Tx_i + b) \leq 1$$

and equation 16 $$ 0 < \alpha_i < C \Rightarrow y_i(w^Tx_i + b) = 1$$



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