Real Algebraic and Analytic Geometry |

On the complexity of Putinar's Positivstellensatz.

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Submission: 2005, October 13.

*Abstract:
We prove an upper bound on the degree complexity of Putinar's Positivstellensatz.
This bound is much worse than the one obtained previously for Schmüdgen's Positivstellensatz
but it depends on the same parameters. As a consequence, we get information about the convergence
rate of Lasserre's procedure for optimization of a polynomial subject to polynomial constraints.*

Mathematics Subject Classification (2000): 11E25, 13J30, 14P10.

Keywords and Phrases: Positivstellensatz, complexity, positive polynomial, sum of squares, preordering, moment problem, optimization of polynomials.

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