If φ γ maps vectors into an infinite-dimensional space, the optimization problem 6-8 is computationally infeasible. Consequentially, we (well, scikit-learn ) computationally solve the dual optimization problem, formulated by using the method of Lagrange multipliers and setting partial derivatives with respect to R, c, and ξ ξ ξ to zero. The dual is an optimization problem over the n Lagrange multipliers α α α involving only the dot product φ γ (m) • φ γ (m ) between mapped feature vectors, which we replace with the kernel k γ (m, m ) that we can compute: