Effects of finite-precision arithmetic on interior-point methods for nonlinear programming.
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, provided that the iterates satisfy centrality and feasibility conditions of the type usually associated with path-following methods. 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. 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.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- SC
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 943273
- Report Number(s):
- ANL/MCS/JA-38782
- Journal Information:
- SIAM J. Optimization, Journal Name: SIAM J. Optimization Journal Issue: 1 ; Oct. 23, 2001 Vol. 12; ISSN 1052-6234
- Country of Publication:
- United States
- Language:
- ENGLISH
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