TSSOS: A Moment-SOS hierarchy that exploits term sparsity

Jie Wang, Victor Magron, Jean-Bernard Lasserre
12/18/2019
math.OC

Official code: wangjie212/TSSOS (69 stars, MIT, last commit 2026-10-20).

Abstract

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 systems literature.

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Code Implementations(1)

wangjie212/TSSOSOfficial100%
MIT

A sparse polynomial optimization tool based on the moment-SOS hierarchy.

6922JuliaSep 30, 20192 days agoMIT

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Cite this paper

@article{wang2019tssos,
  title  = {TSSOS: A Moment-SOS hierarchy that exploits term sparsity},
  author = {Jie Wang and Victor Magron and Jean-Bernard Lasserre},
  year   = {2019},
  eprint = {1912.08899},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1912.08899}
}

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