If your data is not linearly separable, then you have to use the kernel trick, in which case you have to use the dual form. No choice! For data that is linearly separable, there are some quadratic programming algorithms that can solve the dual problem faster than the primal formulation. So in general, I think you should use the dual formulation, unless there is a very specific reason to use the primal form.
Should we use the primal or the dual form of the svm problem to train a model on a training set with millions of instances and hundreds of features
If your data is not linearly separable, then you have to use the kernel trick, in which case you have to use the dual form. No choice! For data that is linearly separable, there are some quadratic programming algorithms that can solve the dual problem faster than the primal formulation. So in general, I think you should use the dual formulation, unless there is a very specific reason to use the primal form.
Is there any effect of the kernel function in the concavity of the Lagrange function?
No, since the Kernel function only modifies the dot-product between x_iand x_i', whereas the concavity is with respect to the alpha parameters.
@@EvolutionaryIntelligence Got it sir. Thank you.