论文标题
Chordal-TSSOS：矩层层次结构，可利用弦扩展的学期稀疏性
Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension
论文作者
论文摘要
这项工作是对ARXIV的后续措施，是ARXIV：1912.08899 [Math.oc]的补充，用于解决多项式优化问题（POPS）。我们提出的Chordal-TSSOS层次结构是基于术语符号和和弦扩展的新的稀疏力矩框架。通过利用输入多项式的项术语，我们获得了半标准编程松弛的两级层次结构。这种弛豫的新颖性和区别特征是获得在迭代过程中获得的准块对基矩阵，该过程执行某些邻接图的弦扩展。这些图与原始数据中产生的术语有关，而与变量之间的链接无关。各种数值示例证明了该新层次结构对不受约束和受约束的POP的效率和可扩展性。这两个层次结构是互补的。前者TSSOS ARXIV：1912.08899 [MATH.OC]具有理论上的融合保证，而Chordal-TSSOS的性能卓越，但缺乏这种理论保证。
This work is a follow-up and a complement to arXiv:1912.08899 [math.OC] for solving polynomial optimization problems (POPs). The chordal-TSSOS hierarchy that we propose is a new sparse moment-SOS framework based on term-sparsity and chordal extension. By exploiting term-sparsity of the input polynomials we obtain a two-level hierarchy of semidefinite programming relaxations. The novelty and distinguishing feature of such relaxations is to obtain quasi block-diagonal matrices obtained in an iterative procedure that performs chordal extension of certain adjacency graphs. The graphs are related to the terms arising in the original data and not to the links between variables. Various numerical examples demonstrate the efficiency and the scalability of this new hierarchy for both unconstrained and constrained POPs. The two hierarchies are complementary. While the former TSSOS arXiv:1912.08899 [math.OC] has a theoretical convergence guarantee, the chordal-TSSOS has superior performance but lacks this theoretical guarantee.
