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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de Klerk, E., Laurent, M., Parrilo, P. On the Equivalence of Algebraic Approaches to the Minimization of Forms on the Simplex. In: Henrion, D., Garulli, A. (eds) Positive Polynomials in Control. Lecture Notes in Control and Information Science, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10997703_7
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DOI: https://doi.org/10.1007/10997703_7
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23948-2
Online ISBN: 978-3-540-31594-0
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