An Interior-Point Perspective on Sensitivity Analysis in Semidefinite
E. Alper Yildirim
We study the asymptotic behavior of the interior-point bounds arising
from the work of Yildirim and Todd on sensitivity analysis in
semidefinite programming in comparison with the optimal partition
bounds. For perturbations of the right-hand side
vector and the cost matrix, we show that the interior-point bounds
evaluated on the central path using the Monteiro-Zhang family of
search directions converge to the symmetrized version of the optimal
partition bounds under appropriate nondegeneracy assumptions, which
can be weaker than the usual notion of nondegeneracy. Furthermore, the
analysis does not assume strict complementarity as long as the central
path converges to the analytic center in a relatively controlled manner.
We also show that the same convergence results carry over to iterates
lying in an
appropriate (very narrow) central path neighborhood if the Nesterov-Todd
is used to evaluate the interior-point bounds.
Technical Report No. 1289, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY 14853-3801.