Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube

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Abstract

We consider the problem of minimizing a polynomial on the hypercube $[0,1]^n$ and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to the Positivstellensatz of Schmüdgen [Math. Ann., 289 (1991), pp. 203–206]. The main tool we employ is Bernstein approximations of polynomials, which also gives constructive proofs and degree bounds for positivity certificates on the hypercube.
Original languageEnglish
Pages (from-to)3104-3120
JournalSIAM Journal on Optimization
Volume20
Issue number6
Publication statusPublished - 2010

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