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Title: Modified Cholesky factorizations in interior-point algorithms for linear programming.

Abstract

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.

Authors:
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
ER
OSTI Identifier:
937894
Report Number(s):
ANL/MCS-P600-0596
Journal ID: ISSN 1052-6234; TRN: US200905%%691
DOE Contract Number:  
DE-AC02-06CH11357
Resource Type:
Journal Article
Journal Name:
SIAM J. Optimization
Additional Journal Information:
Journal Volume: 9; Journal Issue: 4 ; 1999; Journal ID: ISSN 1052-6234
Country of Publication:
United States
Language:
ENGLISH
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; IMPLEMENTATION; LINEAR PROGRAMMING; PERFORMANCE; PERTURBATION THEORY

Citation Formats

Wright, S, and Mathematics and Computer Science. Modified Cholesky factorizations in interior-point algorithms for linear programming.. United States: N. p., 1999. Web. doi:10.1137/S1052623496304712.
Wright, S, & Mathematics and Computer Science. Modified Cholesky factorizations in interior-point algorithms for linear programming.. United States. https://doi.org/10.1137/S1052623496304712
Wright, S, and Mathematics and Computer Science. 1999. "Modified Cholesky factorizations in interior-point algorithms for linear programming.". United States. https://doi.org/10.1137/S1052623496304712.
@article{osti_937894,
title = {Modified Cholesky factorizations in interior-point algorithms for linear programming.},
author = {Wright, S and Mathematics and Computer Science},
abstractNote = {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.},
doi = {10.1137/S1052623496304712},
url = {https://www.osti.gov/biblio/937894}, journal = {SIAM J. Optimization},
issn = {1052-6234},
number = 4 ; 1999,
volume = 9,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 1999},
month = {Fri Jan 01 00:00:00 EST 1999}
}