A sum of squares approximation of nonnegative polynomials

Jean B. Lasserre (lasserrelaas.fr)

Abstract: We show that every real nonnegative polynomial $f$ can be approximated as closely as desired (in the $l_1$-norm of its coefficient vector) by a sequence of polynomials $\{f_\epsilon\}$ that are sums of squares. The novelty is that each $f_\epsilon$ has a simple and explicit form in terms of $f$ and $\epsilon$.

Keywords: Real algebraic geometry; nonnegative polynomials;

Category 1: Global Optimization (Theory )

Category 2: Nonlinear Optimization

Citation: SIAM J. Optimization 16 (2006), 751--765.

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Entry Submitted: 09/23/2005
Entry Accepted: 09/24/2005
Entry Last Modified: 09/18/2006

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