New Complexity Analysis of the Primal-Dual Newton Method for Linear Optimization

J. Peng, C. Roos and T. Terlaky

We deal with the primal-dual Newton method for linear optimization (LO). Nowadays, this method is the workhorse in all efficient interior point algorithms for LO, and its analysis is the basic element in all polynomiality proofs of such algorithms. At present there is still a gap between the practical behavior of the algorithms and the theoretical performance results, in favor of the practical behavior. This is especially true for so-called large-update methods. We present some new analysis tools, based on a proximity measure introduced by Jansen et al., in 1994, that may help to close this gap. This proximity measure has not been used in the analysis of large-update method before. Our new analysis not only provides a unified way for the analysis of both large-update and small-update methods, but also improves the known iteration bounds.

Technical Report 98-05
Delft University of Technology
Faculty of Technical Mathematics and Informatics
P.O. Box 5031, 2600 GA Delft, The Netherlands