Harmonic Hierarchies for Polynomial Optimization
本文为球面上非负形式锥及其对偶矩锥引入了新的多面体逼近层级，证明了收敛速度的可计算定量界，并提出了一种无需优化的算法来构建多项式最小化问题的下界序列。
.We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in \(\mathbb{R}^n\) and for its (dual) cone of moments. We prove computable quantitative bounds on the speed of convergence of such hierarchies. We also introduce a novel optimization-free algorithm for building converging sequences of lower bounds for polynomial minimization problems on spheres. Finally, some computational results are discussed, showcasing our implementation of these hierarchies in the programming language Julia.Keywordspolynomial optimizationlinear hierarchiessemidefinite hierarchiespolynomial kernelsMSC codes90C2690C0590C56