# 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}
}
• Published 1 November 2016
• Mathematics
• Mathematical Programming
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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