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TSSOS: A Moment-SOS hierarchy that exploits term sparsity

Jie Wang 1 Victor Magron 1 Jean-Bernard Lasserre 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
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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https://hal.laas.fr/hal-02448389
Contributor : Victor Magron <>
Submitted on : Wednesday, January 22, 2020 - 11:53:35 AM
Last modification on : Thursday, June 10, 2021 - 3:02:27 AM

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Jie Wang, Victor Magron, Jean-Bernard Lasserre. TSSOS: A Moment-SOS hierarchy that exploits term sparsity. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2021, 31 (1), pp.30--58. ⟨10.1137/19M1307871⟩. ⟨hal-02448389⟩

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