On the complexity of Putinar's Positivstellensatz

Details On the complexity of Putinar's Positivstellensatz On the complexity of Putinar's Positivstellensatz

2008-12-14

arxiv.org/abs/0812.2657v1

Journal of Complexity 23, 1 (2006) 135-150

Mathematics

Algebraic Geometry

Scientific paper

10.1007/10.1016/j.jco.2006.07.00

We prove an upper bound on the degree complexity of Putinar's
Positivstellensatz. This bound is much worse than the one obtained previously
for Schm\"udgen'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.

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