## Semidefinite Programming Relaxations for Semialgebraic Problems (2001)

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Citations: | 225 - 19 self |

### BibTeX

@MISC{Parrilo01semidefiniteprogramming,

author = {Pablo A. Parrilo},

title = {Semidefinite Programming Relaxations for Semialgebraic Problems},

year = {2001}

}

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### 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 provide a constructive approach for finding bounded degree solutions to the Positivstellensatz, and are illustrated with examples from diverse application fields.