Theta Bodies for Polynomial Ideals

@article{Gouveia2010ThetaBF,
  title={Theta Bodies for Polynomial Ideals},
  author={Jo{\~a}o Gouveia and Pablo A. Parrilo and Rekha R. Thomas},
  journal={SIAM Journal on Optimization},
  year={2010},
  volume={20},
  pages={2097-2118}
}
Inspired by a question of Lovász, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lovász’s theta body of the graph. We prove that theta bodies are, up to closure, a version of Lasserre’s relaxations for real solutions to ideals, and that they can be computed explicitly using combinatorial… CONTINUE READING
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