Sparse sums of squares on finite abelian groups and improved semidefinite lifts

@article{Fawzi2016SparseSO,
  title={Sparse sums of squares on finite abelian groups and improved semidefinite lifts},
  author={Hamza Fawzi and James Saunderson and Pablo A. Parrilo},
  journal={Mathematical Programming},
  year={2016},
  volume={160},
  pages={149-191}
}
Let G be a finite abelian group. This paper is concerned with nonnegative functions on G that are sparse with respect to the Fourier basis. We establish combinatorial conditions on subsets $${\mathcal {S}}$$S and $${\mathcal {T}}$$T of Fourier basis elements under which nonnegative functions with Fourier support $${\mathcal {S}}$$S are sums of squares of functions with Fourier support $${\mathcal {T}}$$T. Our combinatorial condition involves constructing a chordal cover of a graph related to G… 

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