An alternative approach for non-linear optimal control problems based on the method of moments
Computational Optimization and Applications
Parameter-dependent Slack variable approach for positivity check of polynomials over hyper-rectangle
ACC'09 Proceedings of the 2009 conference on American Control Conference
Computational Optimization and Applications
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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 $\epsilon$.