On the complexity of Putinar's Positivstellensatz
Algebraic Geometry
2008-12-16 v1 Commutative Algebra
Optimization and Control
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 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.
Keywords
Cite
@article{arxiv.0812.2657,
title = {On the complexity of Putinar's Positivstellensatz},
author = {Jiawang Nie and Markus Schweighofer},
journal= {arXiv preprint arXiv:0812.2657},
year = {2008}
}