@article{eprints2774,
            year = {2015},
           month = {July},
         journal = {IEEE Transactions on Network Science and Engineering},
          volume = {2},
           pages = {97--111},
       publisher = {IEEE},
          author = {Giorgio Gnecco and Rita Morisi and Alberto Bemporad},
           title = {Sparse Solutions to the Average Consensus Problem via Various Regularizations of the Fastest Mixing Markov-Chain Problem},
          number = {3},
             url = {http://eprints.imtlucca.it/2774/},
        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 l{$_1$} -norm and l{$_0$} -?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.},
        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}
}