Sampling Algebraic Varieties for Sum of Squares Programs

@article{Cifuentes2017SamplingAV,
  title={Sampling Algebraic Varieties for Sum of Squares Programs},
  author={Diego Cifuentes and Pablo A. Parrilo},
  journal={SIAM Journal on Optimization},
  year={2017},
  volume={27},
  pages={2381-2404}
}
We study sum of squares (SOS) relaxations to optimize polynomial functions over a set ${\mathcal V}\cap {\mathbb R}^n$, where ${\mathcal V}$ is a complex algebraic variety. We propose a new methodology that, rather than relying on some algebraic description, represents ${\mathcal V}$ with a generic set of complex samples. This approach depends only on the geometry of ${\mathcal V}$, avoiding representation issues such as multiplicity and choice of generators. It also takes advantage of the… CONTINUE READING
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