Modified Cholesky factorizations in interior-point algorithms for linear programming

被引:23
作者
Wright, SJ [1 ]
机构
[1] Argonne Natl Lab, Div Math & Comp Sci, Argonne, IL 60439 USA
关键词
interior-point algorithms and software; Cholesky factorization; matrix perturbations; error analysis;
D O I
10.1137/S1052623496304712
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:1159 / 1191
页数:33
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