Exactness of Parrilo’s Conic Approximations for Copositive Matrices and Associated Low Order Bounds for the Stability Number of a Graph

@article{Laurent2022ExactnessOP,
  title={Exactness of Parrilo’s Conic Approximations for Copositive Matrices and Associated Low Order Bounds for the Stability Number of a Graph},
  author={Monique Laurent and Luis Felipe Vargas},
  journal={Mathematics of Operations Research},
  year={2022}
}
De Klerk and Pasechnik introduced in 2002 semidefinite bounds [Formula: see text] for the stability number [Formula: see text] of a graph G and conjectured their exactness at order [Formula: see text]. These bounds rely on the conic approximations [Formula: see text] introduced by Parrilo in 2000 for the copositive cone [Formula: see text]. A difficulty in the convergence analysis of the bounds is the bad behavior of Parrilo’s cones under adding a zero row/column: when applied to a matrix not… 

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