Application of a Class of Preconditioners to Large Scale Linear Programming Problems

Abstract

In most interior point methods for linear programming, a sequence of weighted linear least squares problems are solved, where the only changes from one iteration to the next are the weights and the right hand side. The weighted least squares problems are usually solved as weighted normal equations by the direct method of Cholesky factorization. In this paper, we consider solving the weighted normal equations by a preconditioned conjugate gradient method at every other iteration. We use a class of preconditioners based on a low rank correction to a Cholesky factorization obtained from the previous iteration. Numerical results show that when properly implemented, the approach of combining direct and iterative methods is promising