Worst-Case Examples for Lasserre's Measure-Based Hierarchy for Polynomial Optimization on the Hypercube

• 成果类型: Article
• 署名作者: de Klerk, Etienne; Laurent, Monique
• 署名单位: Tilburg University; Delft University of Technology; Centrum Wiskunde & Informatica (CWI)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0983
• 发表日期: 2020
• 页码: 86-98
• 关键词: extreme zeros; upper-bounds

摘要

We study the convergence rate of a hierarchy of upper bounds for polynomial optimization problems, proposed by Lasserre, and a related hierarchy by de Klerk, Hess, and Laurent. For polynomial optimization over the hypercube, we show a refined convergence analysis for the first hierarchy. We also show lower bounds on the convergence rate for both hierarchies on a class of examples. These lower bounds match the upper bounds and thus establish the true rate of convergence on these examples. Interestingly, these convergence rates are determined by the distribution of extremal zeroes of certain families of orthogonal polynomials.