  In semidefinite programming a proposed optimal solution may be quite poor in
spite of having sufficiently small residual in the optimality conditions. This
issue may be framed in terms of the discrepancy between forward error (the
unmeasurable `true error') and backward error (the measurable violation of
optimality conditions). In his seminal work, Sturm provided an upper bound on
forward error in terms of backward error and singularity degree. In this paper
we provide a method to bound the maximum rank over all solutions and use this
result to obtain a lower bound on forward error for a class of convergent
sequences. This lower bound complements the upper bound of Sturm. The results
of Sturm imply that semidefinite programs with slow convergence necessarily
have large singularity degree. Here we show that large singularity degree is,
in some sense, also a sufficient condition for slow convergence for a family of
external-type `central' paths. Our results are supported by numerical
observations.
