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

Gennadiy Averkov ()
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Gennadiy Averkov: University of Magdeburg

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 2, No 7, 410-418

Abstract: 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).

Keywords: Polytope; Positivstellensatz; Preordering; Semiring; Quadratic module (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0261-9

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