Preconditioning Indefinite Systems in Interior Point Methods for Optimization

@article{Bergamaschi2004PreconditioningIS,
  title={Preconditioning Indefinite Systems in Interior Point Methods for Optimization},
  author={Luca Bergamaschi and Jacek Gondzio and Giovanni Zilli},
  journal={Comp. Opt. and Appl.},
  year={2004},
  volume={28},
  pages={149-171}
}
Every Newton step in an interior-point method for optimization requires a solution of a symmetric indefinite system of linear equations. Most of today’s codes apply direct solution methods to perform this task. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail to provide sufficient accuracy unless appropriately preconditioned. Two types of preconditioners which use some form of incomplete Cholesky… CONTINUE READING
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