EXPONENTIAL CONVERGENCE OF SUM-OF-SQUARES HIERARCHIES FOR TRIGONOMETRIC POLYNOMIALS

被引：9

作者：

Bach, Francis ^{[1
]}

Rudi, Alessandro ^{[1
]}

机构：

[1] PSL Res Univ, Eole Normale Super, INRIA, Paris, France

来源：

SIAM JOURNAL ON OPTIMIZATION | 2023年 / 33卷 / 03期

基金：

欧洲研究理事会;

关键词：

polynomial optimization; sum of squares; semidefinite programming; SEMIDEFINITE PROGRAMMING RELAXATIONS; OPTIMIZATION;

D O I：

10.1137/22M1540818

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the unconstrained optimization of multivariate trigonometric polynomials by the sum-of-squares hierarchy of lower bounds. We first show a convergence rate of O(1/s(2)) for the relaxation with degree s without any assumption on the trigonometric polynomial to minimize. Second, when the polynomial has a finite number of global minimizers with invertible Hessians at these minimizers, we show an exponential convergence rate with explicit constants. Our results also apply to minimizing regular multivariate polynomials on the hypercube.

引用

页码：2137 / 2159

页数：23

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