Duality: when is dual better than primal? (unclear)


I'm still confused as to which cases are better with dual or with primal. The formulation of the lecture notes is a bit unclear to me Is it:

  • When the dual is a differentiable (but constrained) quadratic problem
  • When we use the kernel trick
  • When alpha is sparse

I'm sorry if this is obvious it just feels like the lecture notes states facts about the dual formulation and I'm not sure if these are always true or if these are what make the dual better than primal in some cases.

Thanks in advance

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