Constructive proofs of some positivstellensätze for compact semialgebraic subsets of ℝ^d

2012/01/19 by Averkov, Gennadiy
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1201.4066

Abstract

In a broad sense, positivstellensätze are results about representations of polynomials which are strictly positive on a given set. We give constructive and, to a large extent, elementary proofs of some known positivstellensätze for compact semialgebraic subsets of ℝ^d. The presented proofs extend and simplify arguments of Berr, Wörmann (2001) and Schweighofer (2002, 2005).

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