Can every convex problem use Lagrangian dual method?

Can every convex problem use Lagrangian dual method?

This is the wrong forum for such general questions since it does not relate to the cvx software. I would post it on

Maybe you should also explain the context a little bit more there.

Thank you very much!

If the Slater condition is not satisfied, there could be a duality gap, which is contrary to the premise under which primal-dual algorithms operate, and which they rely on for termination.