At this time, the maximal margin problem is enhanced as minimizing || w|| 2 /2 + C n i=1 ξ i , where C expresses the weight of errors.
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.