论文标题
多项式优化的谐波层次结构
Harmonic Hierarchies for Polynomial Optimization
论文作者
论文摘要
我们在单位球上以$ \ MATHBB {r}^n $及其（双重）矩锥的（双重）圆锥体介绍了单位球上非负形式的锥的新型多面体近似层次结构。我们证明了此类层次结构收敛速度的可计算定量界限。我们还引入了一种新型的无优化算法，用于在球体上构建多项式最小化问题的下限的收敛序列。最后，讨论了一些计算结果，展示了我们在编程语言Julia中对这些层次结构的实施。
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.
