• Corpus ID: 231894630

An echelon form of weakly infeasible semidefinite programs and bad projections of the psd cone

@article{Pataki2021AnEF,
  title={An echelon form of weakly infeasible semidefinite programs and bad projections of the psd cone},
  author={G{\'a}bor Pataki and Aleksandr Touzov},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.11437}
}
A weakly infeasible semidefinite program (SDP) has no feasible solution, but it has approximate solutions whose constraint violation is arbitrarily small. These SDPs are ill-posed and numerically often unsolvable. They are also closely related to “bad” linear projections that map the cone of positive semidefinite matrices to a nonclosed set. We describe a simple echelon form of weakly infeasible SDPs with the following properties: (i) it is obtained by elementary row operations and congruence… 

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