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  • Krivine–Stengle Positivstellensatz - Wikipedia
    In real algebraic geometry, Krivine–Stengle Positivstellensatz (German for "positive-locus- theorem ") characterizes polynomials that are positive on a semialgebraic set, which is defined by systems of inequalities of polynomials with real coefficients, or more generally, coefficients from any real closed field
  • 6. The Positivstellensatz - MIT - Massachusetts Institute of Technology
    Explicit Formulation of the Positivstellensatz The primal problem is Does there exist x Rn such that fi(x) ̧ 0 for all i = 1; : : : ; m hj (x) = 0 for all j = 1; : : : ; p 2 The dual problem is
  • Positivstellensätze for polynomial matrices with universal quantifiers
    Section 3presents a Scherer-Hol-type Positivstellensatz for polynomial matrices with UQs under the Archimedean condition, along with a sparse version in the presence of correlative sparsity
  • Positivstellensatz - HandWiki
    In real algebraic geometry, Positivstellensatz (German for "positive-locus-theorem") characterizes polynomials that are positive on a semialgebraic set, which is defined by systems of inequalities of polynomials with real coefficients, or more generally, coefficients from any real closed field
  • EE464 Positivstellensatz - Stanford University
    Explicit Formulation of the Positivstellensatz The primal problem is Does there exist x 2 Rn such that fi(x) 0 for all i = 1; : : : ; m hj(x) = 0 for all j = 1; : : : ; p The dual problem is Do there exist ti 2 R[x1; : : : ; xn] and si; rij; : : : 2 such that
  • Degree Bounds for Putinar’s Positivstellensatz on the Hypercube
    3 L Baldi and B Mourrain, On the effective Putinar’s Positivstellensatz and moment approximation, Math Program Ser A, 200 (2023), pp 71–103
  • On the complexity of Putinars Positivstellensatz - ScienceDirect
    Putinar's Positivstellensatz says that, under a certain condition stronger than compactness of S, every real polynomial f positive on S possesses a representation f = ∑ i = 0 m σ i g i where g 0 ≔ 1 and each σ i is a sum of squares of polynomials
  • Positivstellensätze for polynomial matrices - Springer
    Next we propose a matrix version of the Dickinson–Povh Positivstellensatz Finally, we establish a version of Marshall’s theorem for polynomial matrices, approximating positive semi-definite polynomial matrices using sums of squares
  • Positive polynomial - Wikipedia
    The importance of Positivstellensatz theorems in computation arises from its ability to transform problems of polynomial optimization into semidefinite programming problems, which can be efficiently solved using convex optimization techniques [1]
  • An Effective Positivstellensatz over the Rational Numbers for Finite . . .
    View a PDF of the paper titled An Effective Positivstellensatz over the Rational Numbers for Finite Semialgebraic Sets, by Lorenzo Baldi and 2 other authors





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