Yesterday while reviewing the SVM, I understand why we need to transfer the prime form into the dual form. 

The reason is that in the prime form, we have to solve the maximum optimization problem for α firstly, however if we take derivative with respect to α, we would get the original optimization form before we apply Lagrange multiplier, which couldn't be solved. So we have to transfer it into the dual form and take devivate with respect to w firstly. 

However I encountered another question: what's the equal condition that the prime form is equal with dual form? 

(I will take a review for this quesiton today)