A new polynomial-time algorithm for linear programming
Combinatorica
Symmetric indefinite systems for interior point methods
Mathematical Programming: Series A and B
Solving symmetric indefinite systems in an interior-point method for linear programming
Mathematical Programming: Series A and B
Some properties of the Hessian of the logarithmic barrier function
Mathematical Programming: Series A and B
Multiple centrality corrections in a primal-dual method for linear programming
Computational Optimization and Applications
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Stability of Augmented System Factorizations in Interior-Point Methods
SIAM Journal on Matrix Analysis and Applications
Primal-dual interior-point methods
Primal-dual interior-point methods
The cholesky factorization in interior point methods
Computers & Mathematics with Applications
Gigaflops in linear programming
Operations Research Letters
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During the iterations of interior point methods symmetric indefinite systems are decomposed by LD驴L T factorization. This step can be performed in a special way where the symmetric indefinite system is transformed to a positive definite one, called the normal equations system. This approach proved to be efficient in most of the cases and numerically reliable, due to the positive definite property. It has been recognized, however, that in case the linear program contains "dense" columns, this approach results in an undesirable fill---in during the computations and the direct factorization of the symmetric indefinite system is more advantageous. The paper describes a new approach to detect cases where the system of normal equations is not preferable for interior point methods and presents a new algorithm for detecting the set of columns which is responsible for the excessive fill---in in the matrix AA T . By solving large---scale linear programming problems we demonstrate that our heuristic is reliable in practice.