From this paper, I read that
Semidefinite programs can be solved in polynomial time to an arbitrary prescribed precision in the bit model using the ellipsoid method
and
Therefore, interior point algorithms for semidefinite programming are shown to be polynomial in the real number model only, not in the bit number model of computation.
Do we need to assume that Slater condition holds to say interior point algorithms for semidefinite programming are shown to be polynomial in the real number model? So, if the Slater condition fails, then it is still unknown whether or not interior point method can solve SDP in polynomial in the real number model, right?
