REOPTIMIZATION WITH THE PRIMAL-DUAL INTERIOR POINT METHOD.

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