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Constructive Proofs of some Positivstellensätze for Compact Semialgebraic Subsets of ℝ d

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  • Gennadiy Averkov

    (University of Magdeburg)

Abstract

In a broad sense, positivstellensätze are results about representations of polynomials, strictly positive on a given set. We give proofs of some known positivstellensätze for compact semialgebraic subsets of ℝ d , which are to a large extent constructive and elementary. The presented proofs extend and simplify arguments of Berr, Wörmann (Manuscripta Math. 104(2):135–143, 2001) and Schweighofer (J. Pure Appl. Algebra 166(3):307–319, 2002; SIAM J. Optim. 15(3):805–825, 2005).

Suggested Citation

  • Gennadiy Averkov, 2013. "Constructive Proofs of some Positivstellensätze for Compact Semialgebraic Subsets of ℝ d," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 410-418, August.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:2:d:10.1007_s10957-012-0261-9
    DOI: 10.1007/s10957-012-0261-9
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    Cited by:

    1. Matthias Schötz, 2023. "Universal continuous calculus for Su*‐algebras," Mathematische Nachrichten, Wiley Blackwell, vol. 296(6), pages 2588-2608, June.
    2. Amir Ali Ahmadi & Georgina Hall, 2019. "On the Construction of Converging Hierarchies for Polynomial Optimization Based on Certificates of Global Positivity," Management Science, INFORMS, vol. 44(4), pages 1192-1207, November.

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