B.K. Rangarajan and M.J. Todd,
``Convergence of infeasible-interior-point methods for self-scaled conic programming''
Abstract:
We present results on global and polynomial-time convergence of
infeasible-interior-point methods for self-scaled conic programming,
which includes linear and semidefinite programming. First, we establish
global convergence for an algorithm using a wide neighborhood. Next, we
prove polynomial complexity for the algorithm with a slightly narrower
neighborhood. Both neighborhoods are related to the wide (minus
infinity) neighborhood and are much larger than the 2-norm neighborhood.
We also provide stopping rules giving an indication of infeasibility.