Applications of ABS methods to the primal-dual interior point method for linear programming

We consider the application of the ABS procedure to the linear system arising in the primal-dual interior point method where Newton method is used to compute the path to the solution. When approaching the solution the linear system becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS class can reduce the ill conditioning. Preliminary numerical experiments show that the proposed approach can provide a residual in the computed solution up to sixteen orders lower.