I'm reading "The Elements of Statistical Learning", to be precise chapter about optimal separating hyperplanes (SVM classification problem) and I've stuck with the following. I have a function to be maximized:
$$ \sum_{i=1}^{N}a_i - \frac{1}{2}\sum_{i=1}^{N}\sum_{k=1}^{N}a_ia_ky_iy_kx_i^Tx_k, $$
subject to:
$$ 0 = \sum_{i=1}^{N}y_ia_i, \quad b = \sum_{i=1}^{N}a_iy_ix_i, \quad a_i \ge 0 \quad \forall{i}, \quad a_i[y_i(x_i^Tb + b_o) - 1] = 0 \quad \forall{i} $$
And it's written in the book that it's "a simpler convex optimization problem, for which standard software can be used", but I'm not very familiar with optimization methods used in such software.
Could you please suggest which method should I use to find a solution? Which method is commonly used in SVM implementations?
