Let us consider two hyperplanes called separating hyperplanes: (2) (3) can be written in one formula as: Distance from the separating hyperplane to the point xi can be written as: Thus, the margin between two separating hyperplanes can be written as: w,b;xi) xi ;Yi = l xi;yi=--i  To maximize this margin, we should minimize Hwll.
this problem becomes equivalent to solving the following optimization problem: Minimize: Furthermore, this optimization problem can be rewritten into the dual form problem: Find the Lagrange multipliers c~i >_ O(i = 1,..., l) so that: Subject to: In this dual form problem, xi with non-zero ai is called a Support Vector.