eprintid: 2774
rev_number: 8
eprint_status: archive
userid: 69
dir: disk0/00/00/27/74
datestamp: 2015-10-19 09:22:53
lastmod: 2015-10-19 09:22:53
status_changed: 2015-10-19 09:22:53
type: article
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Morisi, Rita
creators_name: Bemporad, Alberto
creators_id: giorgio.gnecco@imtlucca.it
creators_id: rita.morisi@imtlucca.it
creators_id: alberto.bemporad@imtlucca.it
title: Sparse Solutions to the Average Consensus Problem via Various Regularizations of the Fastest Mixing Markov-Chain Problem
ispublished: pub
subjects: QA
subjects: QA75
subjects: T1
divisions: CSA
full_text_status: none
keywords: Artificial neural networks; Convergence; Convex functions; Eigenvalues and eigenfunctions; Optimization; Symmetric matrices; Wireless sensor networks; Consensus; Fastest Mixing Markov-Chain problem; Optimization; Regularization; Sparsity
abstract: In the consensus problem on multi-agent systems, in which the states of the agents represent opinions, the agents aim at reaching a common opinion (or consensus state) through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems to achieve a good trade-off between a small number of interconnections and a fast convergence to the consensus state, which is the average of the initial opinions under mild conditions. This paper addresses this problem through l₁ -norm and l₀ -“pseudo-norm” regularized versions of the well-known Fastest Mixing Markov-Chain (FMMC) problem. We show that such versions can be interpreted as robust forms of the FMMC problem and provide results to guide the choice of the regularization parameter.
date: 2015-07
date_type: published
publication: IEEE Transactions on Network Science and Engineering
volume: 2
number: 3
publisher: IEEE
pagerange: 97-111
id_number: 10.1109/TNSE.2015.2479086
refereed: TRUE
issn: 2327-4697
official_url: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=7268908&filter%3DAND(p_IS_Number%3A7295693)
citation:   Gnecco, Giorgio and Morisi, Rita and Bemporad, Alberto  Sparse Solutions to the Average Consensus Problem via Various Regularizations of the Fastest Mixing Markov-Chain Problem.  IEEE Transactions on Network Science and Engineering, 2 (3).  pp. 97-111.  ISSN 2327-4697      (2015)