# 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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