Avoiding numerical cancellation in the interior point method for solving semidefinite programs

@article{Sturm2003AvoidingNC,
  title={Avoiding numerical cancellation in the interior point method for solving semidefinite programs},
  author={Jos F. Sturm},
  journal={Math. Program.},
  year={2003},
  volume={95},
  pages={219-247}
}
The matrix variables in a primal-dual pair of semidefinite programs are getting increasingly ill-conditioned as they approach a complementary solution. Multiplying the primal matrix variable with a vector from the eigenspace of the non-basic part will therefore result in heavy numerical cancellation. This effect is amplified by the scaling operation in interior point methods. A complete example illustrates these numerical issues. In order to avoid numerical problems in interior point methods… CONTINUE READING

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