Equivariant Semidefinite Lifts and Sum-of-Squares Hierarchies

@article{Fawzi2013EquivariantSL,
  title={Equivariant Semidefinite Lifts and Sum-of-Squares Hierarchies},
  author={Hamza Fawzi and James Saunderson and Pablo A. Parrilo},
  journal={SIAM J. Optim.},
  year={2013},
  volume={25},
  pages={2212-2243}
}
A central question in optimization is to maximize (or minimize) a linear function over a given polytope $P$. To solve such a problem in practice one needs a concise description of the polytope $P$. In this paper we are interested in representations of $P$ using the positive semidefinite cone: a positive semidefinite lift (PSD lift) of a polytope $P$ is a representation of $P$ as the projection of an affine slice of the positive semidefinite cone $\mathbf{S}^d_+$. Such a representation allows… 

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