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On the Equivalence of Algebraic Approaches to the Minimization of Forms on the Simplex

  • Etienne de Klerk
  • Monique Laurent
  • Pablo Parrilo
Part II Algebraic Approaches to Polynomial Positivity
Part of the Lecture Notes in Control and Information Science book series (LNCIS, volume 312)

Abstract

We consider the problem of minimizing a form on the standard simplex [equivalently, the problem of minimizing an even form on the unit sphere]. Two converging hierarchies of approximations for this problem can be constructed, that are based, respectively, on results by Schmüdgen-Putinar and by Pólya about representations of positive polynomials in terms of sums of squares. We show that the two approaches yield, in fact, the same approximations.

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Authors and Affiliations

  • Etienne de Klerk
    • 1
  • Monique Laurent
    • 2
  • Pablo Parrilo
    • 3
  1. 1.University of Waterloo 
  2. 2.CWI, Amsterdam 
  3. 3.Swiss Federal Institute of Technology, Zürich 

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