Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method

Thi-Minh Dung Tran 1 Alain Y. Kibangou 1
1 NECS - Networked Controlled Systems
Inria Grenoble - Rhône-Alpes, GIPSA-DA - Département Automatique
Abstract : This paper presents a new method for estimating the eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system. Given an approximate value of the average of the initial condition of the network state and some intermediate values of the network state when performing a Laplacian-based average consensus, the estimation of the Laplacian eigenvalues is obtained by solving the factorization of the averaging matrix. For this purpose, in contrast to the state of the art, we formulate a convex optimization problem that is solved in a distributed way by means of the Alternating Direction Method of Multipliers (ADMM). The main variables in the optimization problem are the coefficients of a polynomial whose roots are precisely the inverse of the distinct nonzero Laplacian eigenvalues. The performance of the proposed method is evaluated by means of simulation results.
Type de document :
Communication dans un congrès
19th IFAC World Congress (IFAC WC 2014), Aug 2014, Le Cap, South Africa. Proc. of IFAC World Congress 2014, 2014
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https://hal.archives-ouvertes.fr/hal-00968419
Contributeur : Alain Kibangou <>
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Dernière modification le : mardi 15 novembre 2016 - 01:04:07
Document(s) archivé(s) le : lundi 10 avril 2017 - 08:02:06

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Thi-Minh Dung Tran, Alain Y. Kibangou. Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method. 19th IFAC World Congress (IFAC WC 2014), Aug 2014, Le Cap, South Africa. Proc. of IFAC World Congress 2014, 2014. <hal-00968419>

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