Semidefinite programming relaxations for semialgebraic problems

@article{Parrilo2003SemidefinitePR,
  title={Semidefinite programming relaxations for semialgebraic problems},
  author={Pablo A. Parrilo},
  journal={Mathematical Programming},
  year={2003},
  volume={96},
  pages={293-320}
}
  • P. Parrilo
  • Published 1 May 2003
  • Mathematics, Computer Science
  • Mathematical Programming
Abstract. A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility. The main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials, and some results from real algebraic geometry. The techniques… 
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