Document Type
Post-Print
Publication Date
2004
Abstract
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.
Identifier
10.1137/S1052623402409319
Publisher
Society for Industrial and Applied Mathematics
Repository Citation
Holder, A. (2004). Simultaneous data perturbations and analytic center convergence. SIAM Journal on Optimization, 14(3), 841-868. doi:10.1137/S1052623402409319
Publication Information
SIAM Journal on Optimization