Harmonic Hierarchies for Polynomial Optimization

2022/02/25 by Sergio Cristancho, Cristancho, Sergio, Mauricio Velasco +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2202.12865

openalex publication_date 2022/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in ℝⁿ 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.

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