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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This paper concerns some numerical stability issues of factorizations in interior point methods. In our investigation we focus on regularization techniques for the augmented system. We derive the fundamental property of regularization and necessary conditions for the convergence of iterative refinement. A relaxation technique is described that improves on convergence properties. We introduce a practical, adaptive technique to determine the required amount of regularization in numerically difficult situations. Numerical experiments on large-scale, numerically difficult linear programming problems are presented.