Superlinear Convergence of a Stabilized SQP Method to a Degenerate Solution
Computational Optimization and Applications
Detecting "dense" columns in interior point methods for linear programs
Computational Optimization and Applications
Computational Optimization and Applications
On generalized symmetric SOR method for augmented systems
Journal of Computational and Applied Mathematics
Modified SOR-like method for the augmented system
International Journal of Computer Mathematics - Celebrating the Life of David J. Evans
Application of modified homotopy perturbation method for solving the augmented systems
Journal of Computational and Applied Mathematics
A stable primal---dual approach for linear programming under nondegeneracy assumptions
Computational Optimization and Applications
Computational Optimization and Applications
On Interior-Point Warmstarts for Linear and Combinatorial Optimization
SIAM Journal on Optimization
A class of new generalized AOR method for augmented systems
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Evaluation of ST preconditioners for saddle point problems
Journal of Computational and Applied Mathematics
Regularization techniques in interior point methods
Journal of Computational and Applied Mathematics
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Some implementations of interior-point algorithms obtain their search directions by solving symmetric indefinite systems of linear equations. The conditioning of the coefficient matrices in these so-called augmented systems deteriorates on later iterations, as some of the diagonal elements grow without bound. Despite this apparent difficulty, the steps produced by standard factorization procedures are often accurate enough to allow the interior-point method to converge to high accuracy. When the underlying linear program is nondegenerate, we show that convergence to arbitrarily high accuracy occurs, at a rate that closely approximates the theory. We also explain and demonstrate what happens when the linear program is degenerate, where convergence to acceptable accuracy (but not arbitrarily high accuracy) is usually obtained.