As a result, the problem is to maximize the object function D subject to n i=1 λ i y i = 0 and 0 ≤ λ i ≤ C. For the training samples which cannot be separated linearly, they might be separated linearly in higher dimension by mapping them using a nonlinear function: where K( x, x ) is called kernel function.
the object function is rewritten to and the optimal hyperplain is rewritten to Note that φ does not appear in equation 11) (12.