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Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension

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 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.
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Contributor : Victor Magron <>
Submitted on : Monday, March 9, 2020 - 1:42:49 AM
Last modification on : Thursday, June 10, 2021 - 3:07:13 AM

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Jie Wang, Victor Magron, Jean-Bernard Lasserre. Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2021, 31 (1), pp.114--141. ⟨10.1137/20M1323564⟩. ⟨hal-02502131⟩



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