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A Common Symmetrization Framework for Iterative (Linear) Maps

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Geometric Science of Information (GSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

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Abstract

This paper highlights some more examples of maps that follow a recently introduced “symmetrization” structure behind the average consensus algorithm. We review among others some generalized consensus settings and coordinate descent optimization.

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References

  1. Tsitsiklis, J.N.: Problems in decentralized decision making and computation. Ph.D. thesis, MIT (1984)

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  2. Sepulchre, R., Sarlette, A., Rouchon, P.: Consensus in non-commutative spaces. In: Proceedings of 49th IEEE Conference on Decision and Control, pp. 5596–6601 (2010)

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  3. Mazzarella, L., Sarlette, A., Ticozzi, F.: Extending robustness and randomization from consensus to symmetrization algorithms, SIAM J. Control Optim. (2014, in press). http://arxiv.org/abs/1311.3364

  4. Birkhoff, G.: Three observations on linear algebra. Univ. Nac. Tucuan. Rev. A 5, 147–151 (1946)

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  5. Meng, Z., Shi, G., Johansson, K.-H., Cao, M., Yiguang, H.: Modulus consensus over networks with antagonistic interactions and switching topologies (2014). Preprint http://arxiv.org/abs/1402.2766

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Acknowledgments

I thank F.Ticozzi and L.Mazzarella for sharing ideas on the symmetrization approach and R.Sepulchre for encouraging to address these particular applications.

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Authors and Affiliations

  1. QUANTIC, INRIA, Paris Sciences Lettres University, Rocquencourt, France

    Alain Sarlette

Authors
  1. Alain Sarlette
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Correspondence to Alain Sarlette .

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Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Sarlette, A. (2015). A Common Symmetrization Framework for Iterative (Linear) Maps. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_73

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_73

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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