An algorithmic approach to Schmüdgen's Positivstellensatz

DOI10.1016/S0022-4049(01)00041-XzbMath1015.14031OpenAlexW2166822874MaRDI QIDQ5957271

Markus Schweighofer

Publication date: 13 March 2003

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(01)00041-x

zbMATH Keywords

sums of squaressemi-algebraic setSchmüdgen's Positivstellensatzreal closed field

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Ordered rings (13J25) Real algebra (13J30)

Related Items (15)

Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets ⋮ On the complexity of Putinar's Positivstellensatz ⋮ Constructive proofs of some positivstellensätze for compact semialgebraic subsets of \(\mathbb R^{d }\) ⋮ On the complexity of Schmüdgen's Positivstellensatz ⋮ On the Construction of Converging Hierarchies for Polynomial Optimization Based on Certificates of Global Positivity ⋮ Théories géométriques pour l’algèbre des nombres réels ⋮ Effective Pólya semi-positivity for non-negative polynomials on the simplex ⋮ Algorithms for quadratic forms ⋮ Handelman's Positivstellensatz for polynomial matrices positive definite on polyhedra ⋮ An algebraic certificate for Budan's theorem ⋮ A new bound for Pólya's theorem with applications to polynomials positive on polyhedra. ⋮ Pólya's theorem with zeros ⋮ Newton polytopes and relative entropy optimization ⋮ A quantitative Pólya's theorem with zeros ⋮ Completely positive reformulations for polynomial optimization

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