Effects of Finite-Precision Arithmetic on Interior-Point Methods for Nonlinear Programming

We show that the e ects of nite-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. When we replace the standard assumption that the active constraint gradients are independent by the weaker Mangasarian-Fromovitz constraint quali cation, rapid convergence usually is attainable, even when cancellation and roundo errors occur during the calculations. 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. AMS subject classi cations. 90C33, 90C30, 49M45