A ROBUST INTERIOR POINT METHOD FOR COMPUTING THE ANALYTIC CENTER OF AN ILL-CONDITIONED POLYTOPE WITH ERRORS

In this paper we propose an efficient and robust method for computing the analytic center of the polyhedral set P={x€R^n|Ax=b,x>0},where the matrix A€ Rm×n is ill-conditioned,and there are errors in A and b.Besides overcoming the difficulties caused by ill-cond计ioning of the matrix A and errors in A and b,our method can also detect the infeasibility and the unboundedness of the polyhedral set P automatically during the compu tation.Det ailed mat hematical analyses for our method are presen ted and the worst case complexity of the algorithm is also given.Finally some numerical results are presented to show the robustness and effectiveness of the new method.