English

Constructive proofs of some positivstellens\"atze for compact semialgebraic subsets of $\mathbb{R}^d$

Algebraic Geometry 2012-03-14 v2 Commutative Algebra Optimization and Control

Abstract

In a broad sense, positivstellens\"atze 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 positivstellens\"atze for compact semialgebraic subsets of Rd\mathbb{R}^d. The presented proofs extend and simplify arguments of Berr, W\"ormann (2001) and Schweighofer (2002, 2005).

Keywords

Cite

@article{arxiv.1201.4066,
  title  = {Constructive proofs of some positivstellens\"atze for compact semialgebraic subsets of $\mathbb{R}^d$},
  author = {Gennadiy Averkov},
  journal= {arXiv preprint arXiv:1201.4066},
  year   = {2012}
}