Some properties of the Hessian of the logarithmic barrier function
Mathematical Programming: Series A and B
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Modified Cholesky Factorizations in Interior-Point Algorithms for Linear Programming
SIAM Journal on Optimization
Effects of Finite-Precision Arithmetic on Interior-Point Methods for Nonlinear Programming
SIAM Journal on Optimization
Detecting "dense" columns in interior point methods for linear programs
Computational Optimization and Applications
The bpmpd interior point solver for convex quadratically constrained quadratic programming problems
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Regularization techniques in interior point methods
Journal of Computational and Applied Mathematics
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The paper concerns the Cholesky factorization of symmetric positive definite matrices arising in interior point methods. Our investigation is based on a property of the Cholesky factorization which interprets ''small'' diagonal values during factorization as degeneracy in the scaled optimization problem. A practical, scaling independent technique, based on the above property, is developed for the modified Cholesky factorization of interior point methods. This technique increases the robustness of Cholesky factorizations performed during interior point iterations when the optimization problem is degenerate. Our investigations show also the limitations of interior point methods with the recent implementation technology and floating point arithmetic standard. We present numerical results on degenerate linear programming problems of NETLIB.