The central path is an infinitely smooth parameterization of the non-negative real line, and its convergence properties have been investigated since the middle 1980s. However, the central "path" followed by an infeasible-interior-point method relies on three parameters instead of one, and is hence a surface instead of a path. The additional parameters are included to allow for simultaneous perturbations in the cost and righ-hand side vectors. This paper provides a detailed analysis of the perturbed central path that is followed by infeasible-interior-point methods, and we characterize when such a path converges. We develop a set (Hausdorff) convergence property and show that the central paths impose an equivalence relation on the set of admissible cost vectors. We conclude with a technique to test for convergence under arbitrary, simultaneous data perturbations.
Society for Industrial and Applied Mathematics
Holder, A. (2004). Simultaneous data perturbations and analytic center convergence. SIAM Journal on Optimization, 14(3), 841-868. doi:10.1137/S1052623402409319
SIAM Journal on Optimization