The minimization function is indeed "as a fact"; in the sense that it is (somewhat) the formulation of Cortes and Vapnik (http://link.springer.com/article/10.1007%2FBF00994018), which is the main formulation for Support Vector Machines.

The value of 'b' is minimized and the value if found in the first constraint. The value "b\||w||" determines the offset of the hyperplane to the origin and 'w' is the normal vector of that plane.