ABS SOLUTION OF NORMAL EQUATIONS OF SECOND KIND AND APPLICATION TO THE PRIMAL-DUAL INTERIOR POINT METHOD FOR LINEAR PROGRAMMING

We consider on application of the ABS procedure to the linear systems arising from the primal-dual interior point method where Newton methods is used to compute a path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, 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.