Effects of finite-precision arithmetic on
interior-point methods for nonlinear programming
Stephen J. Wright
We show that the effects of finite-precision arithmetic in forming
and solving the linear system that arises at each iteration of
primal-dual interior-point algorithms for nonlinear programming are
benign. Even when we replace the standard assumption that the active
constraint gradients are independent by the weaker
Mangasarian-Fromovitz constraint qualification, rapid convergence
usually is attainable, even when cancellation and roundoff errors
occur during the calculations. This conclusion holds for all three
of the standard formulations of the linear system that is solved at
each iteration of a primal-dual method. In deriving our main
results, we prove a key technical result about the size of the exact
primal-dual step. This result can be used to modify existing
analysis of primal-dual interior-point methods for convex
programming, making it possible to extend the superlinear local
convergence results to the nonconvex case.
Preprint ANL/MCS-P705-0198, Mathematics and Computer
Science Division, Argonne National Laboratory, January, 1998.
Technical Report 98/03, Optimization Tecnology Center, January, 1998.