The dual of the dual of an SDP primal looks identical to the primal problem (algebraically). Then, why is it that in optimization books it is stated that the dual of the dual is a lower bound to the primal problem?
(By algebraically, I mean when I take the dual of the dual it gives me the same problem as the original primal problem. So, the solutions of the two, if they exist, must be the same. Correct?)