Re-optimization with the Primal-Dual Interior Point Method

J. Gondzio and A. Grothey

Re-optimization techniques for an interior point method applied to solve a sequence of linear programming problems are discussed. Conditions are given for problem perturbations that can be absorbed in merely one Newton step. The analysis is performed for both short-step and long-step feasible path-following method. A practical procedure is then derived for an infeasible path-following method. It is applied in the context of {\it crash} start for several large-scale structured linear programs. Numerical results with OOPS, the new object-oriented parallel solver demonstrate the efficiency of the approach. For large structured linear programs crash start leads to about 40\% reduction of the iterations number and translates into 25\% reduction of the solution time. The crash procedure parallelizes well and speed-ups between 3.1-3.8 on 4 processors are achieved.

Technical Report MS-01-004 Department of Mathematics and Statistics, The University of Edinburgh, Scotland. July 27, 2001.