SIAM Journal on Optimization, Volume 31, Issue 1, Page 30-58, January 2021.
This paper is concerned with polynomial optimization problems. We show how to exploit term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of semidefinite programming relaxations. The novelty (and distinguishing feature) of such relaxations is to involve block-diagonal matrices obtained in an iterative procedure performing completion of the connected components of certain adjacency graphs. The graphs are related to the terms arising in the original data and not to the links between variables. Our theoretical framework is then applied to compute lower bounds for polynomial optimization problems either randomly generated or coming from the networked system literature.

中文翻译：

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TSSOS：利用术语稀疏性的时刻-SOS层次结构

SIAM优化杂志，第31卷，第1期，第30-58页，2021年1月。
本文涉及多项式优化问题。我们展示了如何利用输入多项式的项（或多项式）稀疏性来获得半定规划松弛的新收敛层次。这种松弛的新颖性（和显着特征）是涉及在迭代过程中获得的块对角矩阵，该块对角矩阵执行某些邻接图的连接分量的完成。这些图与原始数据中出现的术语相关，而与变量之间的链接无关。然后将我们的理论框架应用于计算多项式优化问题的下界，该多项式优化问题是随机生成的或来自网络系统文献。