Harmonic Hierarchies for Polynomial Optimization
Harmonic Hierarchies for Polynomial Optimization
复制标题
多项式优化的谐波层次
DOI：
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发表时间：
2022
影响因子：
3.1
通讯作者：
Mauricio Velasco
中科院分区：
文献类型：
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作者：
S. Cristancho;Mauricio Velasco
引入了单位球面上非负形式锥在$mathbb{R}^n中及其(对偶)矩锥的新的多面体逼近族.我们证明了这类系统收敛速度的可计算的数量界。我们还介绍了一种新的无优化算法，用于构造球面上多项式极小化问题的下界收敛序列。最后讨论了一些计算结果，展示了我们在程序设计语言Julia中实现这些层次结构。
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.