Harmonic Hierarchies for Polynomial Optimization

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Optimization Pub Date : 2024-02-06 DOI:10.1137/22m1484511

Sergio Cristancho, Mauricio Velasco

引用次数: 0

Abstract

SIAM Journal on Optimization, Volume 34, Issue 1, Page 590-615, March 2024.
Abstract. We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in [math] 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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用于多项式优化的谐波层次结构

SIAM 优化期刊》第 34 卷第 1 期第 590-615 页，2024 年 3 月。摘要我们为[math]中单位球上的非负形式锥及其（对偶）矩锥引入了新的多面体近似层次。我们证明了这种层次收敛速度的可计算定量边界。我们还介绍了一种新颖的免优化算法，用于为球面上的多项式最小化问题建立收敛的下界序列。最后，我们讨论了一些计算结果，并展示了我们在编程语言 Julia 中对这些层次结构的实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Optimization 数学-应用数学

CiteScore

5.30

自引率

9.70%

发文量

101

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.