As far as I understand Support Vector machines, we are trying to find the optimal hyperplane, out of all hyperplanes that are equidistant from the support vectors. There are an infinite number of these hyperplanes, so we can start with an initial hyperplane, H1, which is not optimal. We can then vary the length of the normal vector w, so that we slightly change H1 into H2, which has a larger margin. We continue this process until we find H_max, the hyperplane with maximum margin.
My question is how do I find the initial formula of the first hyperplane H1? Given a linearly separable data set in the plane, how can I calculate a hyperplane that separates the data into two classes and is equidistant from the support vectors? Additionally, I am perhaps forgetting the significance of the variable b in this process.