Positivity and sums of squares: A guide to recent results

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Optimality conditions and finite convergence of Lasserre’s hierarchy (2012, background): “Such problems always exist when the feasible set has dimension three or higher, as shown by Scheiderer [28].”
Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization (2015, unknown): “ber of polynomial inequality constraints were investigated by Krivine [42], Stengle [82], Schmu¨dgen [76], and Putinar [68]. A theorem concerning such polynomials is referred to as Positivstellensatz [75]. For instance, Putinar proved under an assumption slightly stronger than compactness that they ”
Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1‐gain and L∞‐gain characterization (2013, background): “In [44, 45], it is shown that Handelman’s theorem implies Pólya’s theorem [46].”