A Study of Preconditioners for Network Interior Point Methods
Computational Optimization and Applications
Kernel independent component analysis
The Journal of Machine Learning Research
The cholesky factorization in interior point methods
Computers & Mathematics with Applications
On the low-rank approximation by the pivoted Cholesky decomposition
Applied Numerical Mathematics
Regularization techniques in interior point methods
Journal of Computational and Applied Mathematics
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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.