For SVM, it is better to solve the problem in the primal for very large data-sets. However, the non-linear mapping $\phi$ for a RBF kernel is not explicit. Approximation methods for $\phi$ like the Nyström methods are then used.
I am currently working on a classification problem where there is no strong duality (duality gap between the primal and the dual). I have already tested a linear kernel (there $\phi$ is completely explicit: $\phi$(x) = x). I would however be very interested to also test a RBF kernel and then solve the problem in the primal.
=> Can a method like the Nyström method still be applied in my case?