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math.AG2008
On the complexity of Putinar's Positivstellensatz
Jiawang Nie, Markus Schweighofer
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 i…
math.AG2005
Global optimization of polynomials using gradient tentacles and sums of squares
Markus Schweighofer
In this work, the combine the theory of generalized critical values with the theory of iterated rings of bounded elements (real holomorphy rings). We consider the problem of comput…
math.AG2005
On the complexity of Putinar's Positivstellensatz
Jiawang Nie, Markus Schweighofer
This paper has been withdrawn by the author due to its publication