# 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} }

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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