Modified Cholesky factorizations in interior-point algorithms for linear programming.
Journal Article
·
· SIAM J. Optimization
We investigate a modified Cholesky algorithm typical of those used in most interior-point codes for linear programming. Cholesky-based interior-point codes are popular for three reasons: their implementation requires only minimal changes to standard sparse Cholesky algorithms (allowing us to take full advantage of software written by specialists in that area); they tend to be more efficient than competing approaches that use alternative factorizations; and they perform robustly on most practical problems, yielding good interior-point steps even when the coefficient matrix of the main linear system to be solved for the step components is ill conditioned. We investigate this surprisingly robust performance by using analytical tools from matrix perturbation theory and error analysis, illustrating our results with computational experiments. Finally, we point out the potential limitations of this approach.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- ER
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 937894
- Report Number(s):
- ANL/MCS-P600-0596
- Journal Information:
- SIAM J. Optimization, Journal Name: SIAM J. Optimization Journal Issue: 4 ; 1999 Vol. 9; ISSN 1052-6234
- Country of Publication:
- United States
- Language:
- ENGLISH
Similar Records
A parallel formulation of interior point algorithms
Combining interior-point and pivoting algorithms for linear programming
Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP, and SOCP
Book
·
Fri Dec 30 23:00:00 EST 1994
·
OSTI ID:87624
Combining interior-point and pivoting algorithms for linear programming
Conference
·
Fri Dec 30 23:00:00 EST 1994
·
OSTI ID:35765
Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP, and SOCP
Journal Article
·
Fri Aug 15 00:00:00 EDT 2008
· Applied Mathematics and Optimization
·
OSTI ID:21241987