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# Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone

@article{Permenter2018PartialFR, title={Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone}, author={Frank Permenter and Pablo A. Parrilo}, journal={Math. Program.}, year={2018}, volume={171}, pages={1-54} }

- Published 2018 in Math. Program.
DOI:10.1007/s10107-017-1169-9

We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible solution (a frequent output of parsers) by solving a sequence of easier optimization problems and could be a useful pre-processing technique for SDP solvers. We demonstrate effectiveness of the method on SDPs arising in practice, and describe our publicly-available… CONTINUE READING

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